List of Publications

• Work done in the 80's
• Work done in the 90's
• Work done in the 00's
• Work done in the 10's
• Work done in the 20's

• Work done in the 80's
• Work done in the 90's
• Work done in the 00's
• Work done in the 10's
• Work done in the 20's

Books

1. Numerical Methods in Applied Sciences, W. Cai, Z.-C. Shi, C.-W. Shu and J. Xu, editors, Science Press, New York and Beijing, 1996.
2. Advanced Numerical Approximation of Nonlinear Hyperbolic Equations , B. Cockburn, C. Johnson, C.-W. Shu and E. Tadmor (Editor: A. Quarteroni), Lecture Notes in Mathematics, volume 1697, Springer, 1998.
3. Discontinuous Galerkin Methods: Theory, Computation and Applications , B. Cockburn, G. Karniadakis and C.-W. Shu, editors, Lecture Notes in Computational Science and Engineering, volume 11, Springer, 2000.
4. High Order Numerical Methods for the Problems of Aerodynamics (in Russian) , V.I. Pinchukov and C.-W. Shu, Publishing House of the Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia, 2000.
5. Recent Advances in Scientific Computing and Partial Differential Equations , S.Y. Cheng, C.-W. Shu and T. Tang, editors, Contemporary Mathematics, volume 330, American Mathematical Society, 2003.
6. Selected New Numerical Methods for Computational Fluid Dynamics (in Chinese) , R.-X. Liu and C.-W. Shu, Science Press, Beijing, 2003.
7. Recent Advances in Computational Sciences , C.-W. Shu and N. Yan, editors, World Scientific, 2008.
8. Numerical Solutions of Partial Differential Equations , S. Bertoluzza, S. Falletta, G. Russo and C.-W. Shu, Advanced Courses in Mathematics CRM Barcelona, Birkhauser, Basel, 2009.
9. Advances in Mathematics and Its Applications , Y. Li, C.-W. Shu, R. Ye and K. Zuo, Editors, University of Science and Technology of China Press, Hefei, China, 2009.
10. Strong Stability Preserving Runge-Kutta and Multistep Time Discretizations , S. Gottlieb, D. Ketcheson and C.-W. Shu, World Scientific, Singapore, 2011.
11. 75 Years of Mathematics of Computation , S.C. Brenner, I. Shparlinski, C.-W. Shu and D.B. Szyld, Editors, Contemporary Mathematics 754, American Mathematical Society, 2020.

Publications in Refereed Journals (Appeared or Accepted)

1. C.-W. Shu, TVB uniformly high-order schemes for conservation laws , Mathematics of Computation, v49 (1987), pp.105-121.
2. C.-W. Shu, TVB boundary treatment for numerical solutions of conservation laws , Mathematics of Computation, v49 (1987), pp.123-134.
3. C.-W. Shu, Total-variation-diminishing time discretizations , SIAM Journal on Scientific and Statistical Computing, v9 (1988), pp.1073-1084.
4. C.-W. Shu and S. Osher, Efficient implementation of essentially non-oscillatory shock-capturing schemes , Journal of Computational Physics, v77 (1988), pp.439-471.
5. B. Cockburn and C.-W. Shu, TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws II: general framework , Mathematics of Computation, v52 (1989), pp.411-435.
6. C.-W. Shu and S. Osher, Efficient implementation of essentially non- oscillatory shock-capturing schemes II , Journal of Computational Physics, v83 (1989), pp.32-78.
7. B. Cockburn, S.-Y. Lin and C.-W. Shu, TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws III: one-dimensional systems , Journal of Computational Physics, v84 (1989), pp.90-113.
8. W. Cai, D. Gottlieb and C.-W. Shu, Essentially nonoscillatory spectral Fourier methods for shock wave calculations , Mathematics of Computation, v52 (1989), pp.389-410.
9. B. Cockburn, S. Hou and C.-W. Shu, The Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws IV: the multidimensional case , Mathematics of Computation, v54 (1990), pp.545-581.
10. C.-W. Shu, Numerical experiments on the accuracy of ENO and modified ENO schemes , Journal of Scientific Computing, v5 (1990), pp.127-149.
11. B. Cockburn and C.-W. Shu, The Runge-Kutta local projection P1-discontinuous-Galerkin finite element method for scalar conservation laws , Mathematical Modelling and Numerical Analysis (M^2 AN), v25 (1991), pp.337-361.
12. S. Osher and C.-W. Shu, High-order essentially nonoscillatory schemes for Hamilton-Jacobi equations , SIAM Journal on Numerical Analysis, v28 (1991), pp.907-922.
13. C.-W. Shu, A numerical method for systems of conservation laws of mixed type admitting hyperbolic flux splitting , Journal of Computational Physics, v100 (1992), pp.424-429.
14. C.-W. Shu, T.A. Zang, G. Erlebacher, D. Whitaker and S. Osher, High-order ENO schemes applied to two- and three-dimensional compressible flow , Applied Numerical Mathematics, v9 (1992), pp.45-71.
15. W. Cai, D. Gottlieb and C.-W. Shu, On one-sided filters for spectral Fourier approximations of discontinuous functions , SIAM Journal on Numerical Analysis, v29 (1992), pp.905-916.
16. D. Chen, E.C. Kan, U. Ravaioli, C.-W. Shu and R.W. Dutton, An improved energy transport model including nonparabolicity and non-Maxwellian distribution effects , IEEE Electron Device Letters, v13 (1992), pp.26-28.
17. D. Gottlieb, C.-W. Shu, A. Solomonoff and H. Vandeven, On the Gibbs phenomenon I: recovering exponential accuracy from the Fourier partial sum of a nonperiodic analytic function , Journal of Computational and Applied Mathematics, v43 (1992), pp.81-98.
18. W. Cai and C.-W. Shu, Uniform high-order spectral methods for one- and two-dimensional Euler equations , Journal of Computational Physics, v104 (1993), pp.427-443.
19. W. E and C.-W. Shu, Effective equations and the inverse cascade theory for Kolmogorov flows , Physics of Fluids A, v5 (1993), pp.998-1010.
20. W. E and C.-W. Shu, A numerical resolution study of high order essentially non-oscillatory schemes applied to incompressible flow , Journal of Computational Physics, v110 (1994), pp.39-46.
21. B. Cockburn and C.-W. Shu, Nonlinearly stable compact schemes for shock calculations , SIAM Journal on Numerical Analysis, v31 (1994), pp.607-627.
22. G. Jiang and C.-W. Shu, On a cell entropy inequality for discontinuous Galerkin methods , Mathematics of Computation, v62 (1994), pp.531-538.
23. W. E and C.-W. Shu, Small-scale structures in Boussinesq convection , Physics of Fluids, v6 (1994), pp.49-58.
24. J. Casper, C.-W. Shu and H. Atkins, Comparison of two formulations for high-order accurate essentially nonoscillatory schemes , AIAA Journal, v32 (1994), pp.1970-1977.
25. D. Gottlieb and C.-W. Shu, Resolution properties of the Fourier method for discontinuous waves , Computer Methods in Applied Mechanics and Engineering, v116 (1994), pp.27-37.
26. Z. Chen, B. Cockburn, J.W. Jerome and C.-W. Shu, Mixed-RKDG finite element methods for the 2-D hydrodynamic model for semiconductor device simulation , VLSI Design, v3 (1995), pp.145-158.
27. J.W. Jerome and C.-W. Shu, The response of the hydrodynamic model to heat conduction, mobility, and relaxation expressions , VLSI Design, v3 (1995), pp.131-143.
28. D. Gottlieb and C.-W. Shu, On the Gibbs phenomenon IV: recovering exponential accuracy in a subinterval from a Gegenbauer partial sum of a piecewise analytic function , Mathematics of Computation, v64 (1995), pp.1081-1095.
29. C.-W. Shu and P.S. Wong, A note on the accuracy of spectral method applied to nonlinear conservation laws , Journal of Scientific Computing, v10 (1995), pp.357-369.
30. J. Jerome and C.-W. Shu, Transport effects and characteristic modes in the modeling and simulation of submicron devices , IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, v14 (1995), pp.917-923.
31. D. Gottlieb and C.-W. Shu, On the Gibbs phenomenon V: recovering exponential accuracy from collocation point values of a piecewise analytic function , Numerische Mathematik, v71 (1995), pp.511-526.
32. D.P. Chen, R.S. Eisenberg, J.W. Jerome and C.-W. Shu, Hydrodynamic model of temperature change in open ionic channels , Biophysical Journal, v69 (1995), pp.2304-2322.
33. D. Gottlieb and C.-W. Shu, On the Gibbs phenomenon III: recovering exponential accuracy in a sub-interval from a spectral partial sum of a piecewise analytic function , SIAM Journal on Numerical Analysis, v33 (1996), pp.280-290.
34. B. Perthame and C.-W. Shu, On positive preserving finite volume schemes for Euler equations , Numerische Mathematik, v73 (1996), pp.119-130.
35. E. Harabetian, S. Osher and C.-W. Shu, An Eulerian approach for vortex motion using a level set regularization procedure , Journal of Computational Physics, v127 (1996), pp.15-26.
36. G.-S. Jiang and C.-W. Shu, Efficient implementation of weighted ENO schemes , Journal of Computational Physics, v126 (1996), pp.202-228.
37. C.-W. Shu and Y. Zeng, High order essentially non-oscillatory scheme for viscoelasticity with fading memory , Quarterly of Applied Mathematics, v55 (1997), pp.459-484.
38. G. Erlebacher, M.Y. Hussaini and C.-W. Shu, Interaction of a shock with a longitudinal vortex , Journal of Fluid Mechanics, v337 (1997), pp.129-153.
39. D. Gottlieb and C.-W. Shu, On the Gibbs phenomenon and its resolution , SIAM Review, v30 (1997), pp.644-668.
40. K. Siddiqi, B.B. Kimia and C.-W. Shu, Geometric shock-capturing ENO schemes for subpixel interpolation, computation and curve evolution , Graphical Models and Image Processing (CVGIP:GMIP), v59 (1997), pp.278-301.
41. S. Gottlieb and C.-W. Shu, Total variation diminishing Runge-Kutta schemes , Mathematics of Computation, v67 (1998), pp.73-85.
42. B. Cockburn and C.-W. Shu, The Runge-Kutta discontinuous Galerkin method for conservation laws V: multidimensional systems , Journal of Computational Physics, v141 (1998), pp.199-224.
43. H.L. Atkins and C.-W. Shu, Quadrature-free implementation of discontinuous Galerkin method for hyperbolic equations , AIAA Journal, v36 (1998), pp.775-782.
44. G.-Q. Chen, J.W. Jerome and C.-W. Shu, Analysis and simulation of extended hydrodynamic models: the multi-valley Gunn oscillator and MESFET symmetries , VLSI Design, v6 (1998), pp.277-282.
45. C. Cercignani, I.M. Gamba, J.W. Jerome and C.-W. Shu, Applicability of the high field model: an analytical study via asymptotic parameters defining domain decomposition , VLSI Design, v8 (1998), pp.135-141.
46. C. Cercignani, I.M. Gamba, J.W. Jerome and C.-W. Shu, Applicability of the high field model: a preliminary numerical study , VLSI Design, v8 (1998), pp.275-282.
47. B. Cockburn and C.-W. Shu, The local discontinuous Galerkin method for time-dependent convection-diffusion systems , SIAM Journal on Numerical Analysis, v35 (1998), pp.2440-2463.
48. P. Montarnal and C.-W. Shu, Real gas computation using an energy relaxation method and high-order WENO schemes , Journal of Computational Physics, v148 (1999), pp.59-80.
49. C. Hu and C.-W. Shu, Weighted essentially non-oscillatory schemes on triangular meshes , Journal of Computational Physics, v150 (1999), pp.97-127.
50. C. Hu and C.-W. Shu, A discontinuous Galerkin finite element method for Hamilton-Jacobi equations , SIAM Journal on Scientific Computing, v21 (1999), pp.666-690.
51. O. Lepsky, C. Hu and C.-W. Shu, The Analysis of the discontinuous Galerkin method for Hamilton-Jacobi equations , Applied Numerical Mathematics, v33 (2000), pp.423-434.
52. C. Cercignani, I.M. Gamba, J.W. Jerome and C.-W. Shu, Device benchmark comparisons via kinetic, hydrodynamic, and high-field models , Computer Methods in Applied Mechanics and Engineering, v181 (2000), pp.381-392.
53. D.S. Balsara and C.-W. Shu, Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy , Journal of Computational Physics, v160 (2000), pp.405-452.
54. J.-G. Liu and C.-W. Shu, A high-order discontinuous Galerkin method for 2D incompressible flows , Journal of Computational Physics, v160 (2000), pp.577-596.
55. C. Cercignani, I.M. Gamba, J.W. Jerome and C.-W. Shu, A domain decomposition method for silicon devices , Transport Theory and Statistical Physics, v29 (2000), pp.525-536.
56. J.A. Carrillo, I.M. Gamba and C.-W. Shu, Computational macroscopic approximations to the one-dimensional relaxation-time kinetic system for semiconductors , Physica D, v146 (2000), pp.289-306.
57. S. Gottlieb, C.-W. Shu and E. Tadmor, Strong stability-preserving high-order time discretization methods , SIAM Review, v43 (2001), pp.89-112.
58. T. Zhou, Y. Guo and C.-W. Shu, Numerical study on Landau damping , Physica D, v157 (2001), pp.322-333.
59. A. Arnold, J.A. Carrillo, I. Gamba and C.-W. Shu, Low and high field scaling limits for the Vlasov- and Wigner-Poisson-Fokker-Planck systems , Transport Theory and Statistical Physics, v30 (2001), pp.121-153.
60. T. Zhou, Y. Li and C.-W. Shu, Numerical comparison of WENO finite volume and Runge-Kutta discontinuous Galerkin methods , Journal of Scientific Computing, v16 (2001), pp.145-171.
61. B. Cockburn and C.-W. Shu, Runge-Kutta Discontinuous Galerkin methods for convection-dominated problems , Journal of Scientific Computing, v16 (2001), pp.173-261.
62. M.A. Anile, J.A. Carrillo, I.M. Gamba and C.-W. Shu, Approximation of the BTE by a relaxation-time operator: simulations for a 50nm-channel Si diode , VLSI Design, v13 (2001), pp.349-354.
63. K. Banoo, J.-H. Rhew, M. Lundstrom, C.-W. Shu and J.W. Jerome, Simulating quasi-ballistic transport in Si nanotransistors , VLSI Design, v13 (2001), pp.5-13.
64. J. Shi, C. Hu and C.-W. Shu, A technique of treating negative weights in WENO schemes , Journal of Computational Physics, v175 (2002), pp.108-127.
65. J. Yan and C.-W. Shu, A local discontinuous Galerkin method for KdV type equations , SIAM Journal on Numerical Analysis, v40 (2002), pp.769-791.
66. J. Yan and C.-W. Shu, Local discontinuous Galerkin methods for partial differential equations with higher order derivatives , Journal of Scientific Computing, v17 (2002), pp.27-47.
67. J.A. Carrillo, I.M. Gamba, A. Majorana and C.-W. Shu, A WENO-solver for the 1D non-stationary Boltzmann-Poisson system for semiconductor devices , Journal of Computational Electronics, v1 (2002), pp.365-370.
68. P. Lin and C.-W. Shu, Numerical solution of a virtual internal bond model for material fracture , Physica D, v167 (2002), pp.101-121.
69. J. Qiu and C.-W. Shu, On the construction, comparison, and local characteristic decomposition for high-order central WENO schemes , Journal of Computational Physics, v183 (2002), pp.187-209.
70. G.-D. Jin, D.-Y. Liu and C.-W. Shu, Propagation and decay of concentration wave in the liquid-solid pulsed fluidized beds , The Chinese Journal of Process Engineering (in Chinese), v2 (2002), pp.392-399.
71. C.-W. Shu, High-order finite difference and finite volume WENO schemes and discontinuous Galerkin methods for CFD , International Journal of Computational Fluid Dynamics, v17 (2003), pp.107-118.
72. B. Cockburn, M. Luskin, C.-W. Shu and E. Suli, Enhanced accuracy by post-processing for finite element methods for hyperbolic equations , Mathematics of Computation, v72 (2003), pp.577-606.
73. M.H. Carpenter, D. Gottlieb and C.-W. Shu, On the conservation and convergence to weak solutions of global schemes , Journal of Scientific Computing, v18 (2003), pp.111-132.
74. Y.-T. Zhang and C.-W. Shu, High order WENO schemes for Hamilton-Jacobi equations on triangular meshes , SIAM Journal on Scientific Computing, v24 (2003), pp.1005-1030.
75. J.A. Carrillo, I.M. Gamba, A. Majorana and C.-W. Shu, A WENO-solver for the transients of Boltzmann-Poisson system for semiconductor devices: performance and comparisons with Monte Carlo methods , Journal of Computational Physics, v184 (2003), pp.498-525.
76. R.P. Fedkiw, G. Sapiro and C.-W. Shu, Shock capturing, level sets, and PDE based methods in computer vision and image processing: a review of Osher's contributions , Journal of Computational Physics, v185 (2003), pp.309-341.
77. K. Sebastian and C.-W. Shu, Multidomain WENO finite difference method with interpolation at subdomain interfaces , Journal of Scientific Computing, v19 (2003), pp.405-438.
78. M. Zhang and C.-W. Shu, An analysis of three different formulations of the discontinuous Galerkin method for diffusion equations , Mathematical Models and Methods in Applied Sciences, v13 (2003), pp.395-413.
79. J. Shi, Y.-T. Zhang and C.-W. Shu, Resolution of high order WENO schemes for complicated flow structures , Journal of Computational Physics, v186 (2003), pp.690-696.
80. J. Qiu and C.-W. Shu, Finite difference WENO schemes with Lax-Wendroff-type time discretizations , SIAM Journal on Scientific Computing, v24 (2003), pp.2185-2198.
81. M. Zhang, C.-W. Shu, G.C.K. Wong and S.C. Wong, A weighted essentially non-oscillatory numerical scheme for a multi-class Lighthill-Whitham-Richards traffic flow model , Journal of Computational Physics, v191 (2003), pp.639-659.
82. Y.-T. Zhang, J. Shi, C.-W. Shu and Y. Zhou, Numerical viscosity and resolution of high-order weighted essentially nonoscillatory schemes for compressible flows with high Reynolds numbers , Physical Review E, v68 (2003), 046709.
83. J. Qiu and C.-W. Shu, Hermite WENO schemes and their application as limiters for Runge-Kutta discontinuous Galerkin method: one dimensional case , Journal of Computational Physics, v193 (2003), pp.115-135.
84. J.A. Carrillo, I.M. Gamba, A. Majorana and C.-W. Shu, A direct solver for 2D non-stationary Boltzmann-Poisson systems for semiconductor devices: a MESFET simulation by WENO-Boltzmann schemes , Journal of Computational Electronics, v2 (2003), pp.375-380.
85. J. Ryan and C.-W. Shu, On a one-sided post-processing technique for the discontinuous Galerkin methods , Methods and Applications of Analysis, v10 (2003), pp.295-308.
86. Q. Zhang, M. Zhang, G. Jin, D. Liu and C.-W. Shu, Modeling, numerical methods, and simulation for particle-fluid two-phase flow problems , Computers and Mathematics with Applications, v47 (2004), pp.1437-1462.
87. Y. Guo, C.-W. Shu and T. Zhou, The dynamics of a plane diode , SIAM Journal on Mathematical Analysis, v35 (2004), pp.1617-1635.
88. B. Cockburn, F. Li and C.-W. Shu, Locally divergence-free discontinuous Galerkin methods for the Maxwell equations , Journal of Computational Physics, v194 (2004), pp.588-610.
89. Q. Zhang and C.-W. Shu, Error estimates to smooth solutions of Runge-Kutta discontinuous Galerkin methods for scalar conservation laws , SIAM Journal on Numerical Analysis, v42 (2004), pp.641-666.
90. D. Levy, C.-W. Shu and J. Yan, Local discontinuous Galerkin methods for nonlinear dispersive equations , Journal of Computational Physics, v196 (2004), pp.751-772.
91. Y. Xu and C.-W. Shu, Local discontinuous Galerkin methods for three classes of nonlinear wave equations , Journal of Computational Mathematics, v22 (2004), pp.250-274.
92. L.-L. Feng, C.-W. Shu and M. Zhang, A hybrid cosmological hydrodynamic/N-body code based on a weighted essentially nonoscillatory scheme , Astrophysical Journal, v612 (2004), pp.1-13.
93. Y. Liu and C.-W. Shu, Local discontinuous Galerkin methods for moment models in device simulations: formulation and one dimensional results , Journal of Computational Electronics, v3 (2004), pp.263-267.
94. F. Li and C.-W. Shu, Locally divergence-free discontinuous Galerkin methods for MHD equations , Journal of Scientific Computing, v22-23 (2005), pp.413-442.
95. M. Zhang and C.-W. Shu, An analysis of and a comparison between the discontinuous Galerkin and the spectral finite volume methods , Computers and Fluids, v34 (2005), pp.581-592.
96. Y. Ha, C.L. Gardner, A. Gelb and C.-W. Shu, Numerical simulation of high Mach number astrophysical jets with radiative cooling , Journal of Scientific Computing, v24 (2005), pp.597-612.
97. C.-W. Shu, W.-S. Don, D. Gottlieb, O. Schilling and L. Jameson, Numerical convergence study of nearly incompressible, inviscid Taylor-Green vortex flow , Journal of Scientific Computing, v24 (2005), pp.569-595.
98. J. Ryan, C.-W. Shu and H. Atkins, Extension of a postprocessing technique for the discontinuous Galerkin method for hyperbolic equations with application to an aeroacoustic problem , SIAM Journal on Scientific Computing, v26 (2005), pp.821-843.
99. J. Qiu and C.-W. Shu, Runge-Kutta discontinuous Galerkin method using WENO limiters , SIAM Journal on Scientific Computing, v26 (2005), pp.907-929.
100. J. Qiu and C.-W. Shu, Hermite WENO schemes and their application as limiters for Runge-Kutta discontinuous Galerkin method II: two dimensional case , Computers and Fluids, v34 (2005), pp.642-663.
101. J. Qiu and C.-W. Shu, Hermite WENO schemes for Hamilton-Jacobi equations , Journal of Computational Physics, v204 (2005), pp.82-99.
102. F. Li and C.-W. Shu, Reinterpretation and simplified implementation of a discontinuous Galerkin method for Hamilton-Jacobi equations , Applied Mathematics Letters, v18 (2005), pp.1204-1209.
103. Y. Xu and C.-W. Shu, Local discontinuous Galerkin methods for nonlinear Schrodinger equations , Journal of Computational Physics, v205 (2005), pp.72-97.
104. S. Chen, W. E and C.-W. Shu, The heterogeneous multiscale method based on the discontinuous Galerkin method for hyperbolic and parabolic problems , Multiscale Modeling and Simulation, v3 (2005), pp.871-894.
105. Z. Xu and C.-W. Shu, Anti-diffusive flux corrections for high order finite difference WENO schemes , Journal of Computational Physics, v205 (2005), pp.458-485.
106. J. Qiu, M. Dumbser and C.-W. Shu, The discontinuous Galerkin method with Lax-Wendroff type time discretizations , Computer Methods in Applied Mechanics and Engineering, v194 (2005), pp.4528-4543.
107. Y. Xing and C.-W. Shu, High order finite difference WENO schemes with the exact conservation property for the shallow water equations , Journal of Computational Physics, v208 (2005), pp.206-227.
108. L.-L. Feng, P. He, L. Fang, C.-W. Shu and M. Zhang, Intergalactic medium in the $\Lambda$CDM universe from cosmological simulations , Journal of the Korean Astronomical Society, v38 (2005), pp.129-132.
109. F. Filbet and C.-W. Shu, Approximation of hyperbolic models for chemosensitive movement , SIAM Journal on Scientific Computing, v27 (2005), pp.850-872.
110. J. Qiu and C.-W. Shu, A comparison of troubled-cell indicators for Runge-Kutta discontinuous Galerkin methods using weighted essentially nonoscillatory limiters , SIAM Journal on Scientific Computing, v27 (2005), pp.995-1013.
111. Y. Xu and C.-W. Shu, Local discontinuous Galerkin methods for two classes of two-dimensional nonlinear wave equations , Physica D, v208 (2005), pp.21-58.
112. S. Zhang, Y.-T. Zhang and C.-W. Shu, Multistage interaction of a shock wave and a strong vortex , Physics of Fluids, v17 (2005), 116101.
113. F. Filbet, Y. Guo and C.-W. Shu, Analysis of the relativistic Vlasov-Maxwell model in an interval , Quarterly of Applied Mathematics, v63 (2005), pp.691-714.
114. Z. Xu and C.-W. Shu, Anti-diffusive high order WENO schemes for Hamilton-Jacobi equations , Methods and Applications of Analysis, v12 (2005), pp.169-190.
115. Y. Xu and C.-W. Shu, Local discontinuous Galerkin methods for the Kuramoto-Sivashinsky equations and the Ito-type coupled KdV equations , Computer Methods in Applied Mechanics and Engineering, v195 (2006), pp.3430-3447.
116. J. Qiu, B.C. Khoo and C.-W. Shu, A numerical study for the performance of the Runge-Kutta discontinuous Galerkin method based on different numerical fluxes , Journal of Computational Physics, v212 (2006), pp.540-565.
117. P. Zhang, S.C. Wong and C.-W. Shu, A weighted essentially non-oscillatory numerical scheme for a multi-class traffic flow model on an inhomogeneous highway , Journal of Computational Physics, v212 (2006), pp.739-756.
118. J.A. Carrillo, I.M. Gamba, A. Majorana and C.-W. Shu, 2D semiconductor device simulations by WENO-Boltzmann schemes: efficiency, boundary conditions and comparison to Monte Carlo methods , Journal of Computational Physics, v214 (2006), pp.55-80.
119. Y. Xing and C.-W. Shu, High-order well-balanced finite difference WENO schemes for a class of hyperbolic systems with source terms , Journal of Scientific Computing, v27 (2006), pp.477-494.
120. Y. Xing and C.-W. Shu, High order well-balanced finite volume WENO schemes and discontinuous Galerkin methods for a class of hyperbolic systems with source terms , Journal of Computational Physics, v214 (2006), pp.567-598.
121. Y. Xing and C.-W. Shu, A new approach of high order well-balanced finite volume WENO schemes and discontinuous Galerkin methods for a class of hyperbolic systems with source terms , Communications in Computational Physics, v1 (2006), pp.101-135.
122. S. Gottlieb, D. Gottlieb and C.-W. Shu, Recovering high-order accuracy in WENO computations of steady-state hyperbolic systems , Journal of Scientific Computing, v28 (2006), pp.307-318.
123. C.-S. Chou and C.-W. Shu, High order residual distribution conservative finite difference WENO schemes for steady state problems on non-smooth meshes , Journal of Computational Physics, v214 (2006), pp.698-724.
124. K. Kremeyer, K. Sebastian and C.-W. Shu, Computational study of shock mitigation and drag reduction by pulsed energy lines, , AIAA Journal, v44 (2006), pp.1720-1731.
125. P. He, J. Liu, L.-L. Feng, C.-W. Shu and L.-Z. Fang, Low-redshift cosmic baryon fluid on large scales and She-Leveque universal scaling , Physical Review Letters, v96 (2006), 051302.
126. L. Yuan and C.-W. Shu, Discontinuous Galerkin method based on non-polynomial approximation spaces , Journal of Computational Physics, v218 (2006), pp.295-323.
127. Z. Xu and C.-W. Shu, Anti-diffusive finite difference WENO methods for shallow water with transport of pollutant , Journal of Computational Mathematics, v24 (2006), pp.239-251.
128. Y.-T. Zhang, C.-W. Shu and Y. Zhou, Effects of shock waves on Rayleigh-Taylor instability , Physics of Plasmas, v13 (2006), 062705.
129. J.-M. Qiu, C.-W. Shu, L.-L. Feng and L.-Z. Fang, A WENO algorithm for the radiative transfer and ionized sphere at reionization , New Astronomy, v12 (2006), pp.1-10.
130. Q. Zhang and C.-W. Shu, Error estimates to smooth solutions of Runge-Kutta discontinuous Galerkin method for symmetrizable systems of conservation laws , SIAM Journal on Numerical Analysis, v44 (2006), pp.1703-1720.
131. Y. Xing and C.-W. Shu, Application of high order well-balanced schemes to a class of hyperbolic systems with source terms , Boletin de la Sociedad Espanola de Matematica Aplicada, v34 (2006), pp.69-80.
132. S. Zhang, Y.-T. Zhang and C.-W. Shu, Interaction of an oblique shock wave with a pair of parallel vortices: shock dynamics and mechanism of sound generation , Physics of Fluids, v18 (2006), 126101.
133. D. Levy, S. Nayak, C.-W. Shu and Y.-T. Zhang, Central WENO schemes for Hamilton-Jacobi equations on triangular meshes , SIAM Journal on Scientific Computing, v28 (2006), pp.2229-2247.
134. M.J. Caceres, J.A. Carrillo, I. Gamba, A. Majorana and C.-W. Shu, DSMC versus WENO-BTE: a double gate MOSFET example , Journal of Computational Electronics, v5 (2006), pp.471-474.
135. F. Li and C.-W. Shu, A local-structure-preserving local discontinuous Galerkin method for the Laplace equation , Methods and Applications of Analysis, v13 (2006), pp.215-234.
136. Y. Liu and C.-W. Shu, Local discontinuous Galerkin methods for moment models in device simulations: performance assessment and two dimensional results , Applied Numerical Mathematics, v57 (2007), pp.629-645.
137. S. Zhang and C.-W. Shu, A new smoothness indicator for the WENO schemes and its effect on the convergence to steady state solutions , Journal of Scientific Computing, v31 (2007), pp.273-305.
138. Y. Cheng and C.-W. Shu, A discontinuous Galerkin finite element method for directly solving the Hamilton-Jacobi equations , Journal of Computational Physics, v223 (2007), pp.398-415.
139. J. Shen, C.-W. Shu and M. Zhang, High resolution schemes for a hierarchical size-structured model , SIAM Journal on Numerical Analysis, v45 (2007), pp.352-370.
140. C.-S. Chou and C.-W. Shu, High order residual distribution conservative finite difference WENO schemes for convection-diffusion steady state problems on non-smooth meshes , Journal of Computational Physics, v224 (2007), pp.992-1020.
141. Y. Xu and C.-W. Shu, Error estimates of the semi-discrete local discontinuous Galerkin method for nonlinear convection-diffusion and KdV equations , Computer Methods in Applied Mechanics and Engineering, v196 (2007), pp.3805-3822.
142. J.-M. Qiu, L.-L. Feng, C.-W. Shu and L.-Z. Fang, A WENO algorithm of the temperature and ionization profiles around a point source , New Astronomy, v12 (2007), pp.398-409.
143. Y. Liu, C.-W. Shu, E. Tadmor and M. Zhang, Non-oscillatory hierarchical reconstruction for central and finite volume schemes , Communications in Computational Physics, v2 (2007), pp.933-963.
144. Y. Xia, Y. Xu and C.-W. Shu, Efficient time discretization for local discontinuous Galerkin methods , Discrete and Continuous Dynamical Systems - Series B, v8 (2007), pp.677-693.
145. S. Chen, W. E, Y. Liu and C.-W. Shu, A discontinuous Galerkin implementation of a domain decomposition method for kinetic-hydrodynamic coupling multiscale problems in gas dynamics and device simulations , Journal of Computational Physics, v225 (2007), pp.1314-1330.
146. J. Liu, J.-M. Qiu, L.-L. Feng, C.-W. Shu and L.-Z. Fang, 21 cm signals from early ionizing sources , The Astrophysical Journal, v663 (2007), pp.1-9.
147. S. Noelle, Y. Xing and C.-W. Shu, High-order well-balanced finite volume WENO schemes for shallow water equation with moving water , Journal of Computational Physics, v226 (2007), pp.29-58.
148. Y. Xia, Y. Xu and C.-W. Shu, Local discontinuous Galerkin methods for the Cahn-Hilliard type equations , Journal of Computational Physics, v227 (2007), pp.472-491.
149. J. Shen, C.-W. Shu and M. Zhang, A high order WENO scheme for a hierarchical size-structured population model , Journal of Scientific Computing, v33 (2007), pp.279-291.
150. J. Cheng and C.-W. Shu, A high order ENO conservative Lagrangian type scheme for the compressible Euler equations , Journal of Computational Physics, v227 (2007), pp.1567-1596.
151. Y. Liu, C.-W. Shu, E. Tadmor and M. Zhang, Central discontinuous Galerkin methods on overlapping cells with a nonoscillatory hierarchical reconstruction , SIAM Journal on Numerical Analysis, v45 (2007), pp.2442-2467.
152. S. Curtis, R.M. Kirby, J.K. Ryan and C.-W. Shu, Postprocessing for the discontinuous Galerkin method over nonuniform meshes , SIAM Journal on Scientific Computing, v30 (2008), pp.272-289.
153. J. Cheng and C.-W. Shu, A high order accurate conservative remapping method on staggered meshes , Applied Numerical Mathematics, v58 (2008), pp.1042-1060.
154. Y. Cheng and C.-W. Shu, A discontinuous Galerkin finite element method for time dependent partial differential equations with higher order derivatives , Mathematics of Computation, v77 (2008), pp.699-730.
155. Y. Xu and C.-W. Shu, A local discontinuous Galerkin method for the Camassa-Holm equation , SIAM Journal on Numerical Analysis, v46 (2008), pp.1998-2021.
156. J.-M. Qiu and C.-W. Shu, Convergence of Godunov-type schemes for scalar conservation laws under large time steps , SIAM Journal on Numerical Analysis, v46 (2008), pp.2211-2237.
157. J.-M. Qiu, C.-W. Shu, J.-R. Liu and L.-Z. Fang, A WENO algorithm for the growth of ionized regions at the reionization epoch , New Astronomy, v13 (2008), pp.1-11.
158. L. Yuan and C.-W. Shu, Discontinuous Galerkin method for a class of elliptic multi-scale problems , International Journal for Numerical Methods in Fluids, v56 (2008), pp.1017-1032.
159. W. Chen, S.C. Wong and C.-W. Shu, Efficient implementation of the shock-fitting algorithm for the Lighthill-Whitham-Richards traffic flow model , International Journal for Numerical Methods in Engineering, v74 (2008), pp.554-600.
160. Y. Lu, S.C. Wong, M. Zhang, C.-W. Shu and W. Chen, Explicit construction of entropy solutions for the Lighthill-Whitham-Richards traffic flow model with a piecewise quadratic flow-density relationship , Transportation Research Part B, v42 (2008), pp.355-372.
161. Y. Liu, C.-W. Shu and M. Zhang, Strong stability preserving property of the deferred correction time discretization , Journal of Computational Mathematics, v26 (2008), pp.633-656.
162. W. Wang, X. Li and C.-W. Shu, The discontinuous Galerkin method for the multiscale modeling of dynamics of crystalline solids , Multiscale Modeling and Simulation, v7 (2008), pp.294-320.
163. J. Zhu, J. Qiu, C.-W. Shu and M. Dumbser, Runge-Kutta discontinuous Galerkin method using WENO limiters II: unstructured meshes , Journal of Computational Physics, v227 (2008), pp.4330-4353.
164. Y. Liu, C.-W. Shu, E. Tadmor and M. Zhang, $L^2$ stability analysis of the central discontinuous Galerkin method and a comparison between the central and regular discontinuous Galerkin methods , ESAIM: Mathematical Modelling and Numerical Analysis (M^2 AN), v42 (2008), pp.593-607.
165. Y. Xia, S.C. Wong, M. Zhang, C.-W. Shu and W.H.K. Lam, An efficient discontinuous Galerkin method on triangular meshes for a pedestrian flow model , International Journal for Numerical Methods in Engineering, v76 (2008), pp.337-350.
166. J. Cheng and C.-W. Shu, A third order conservative Lagrangian type scheme on curvilinear meshes for the compressible Euler equations , Communications in Computational Physics, v4 (2008), pp.1008-1024.
167. L. Huang, C.-W. Shu and M. Zhang, Numerical boundary conditions for the fast sweeping high order WENO methods for solving the Eikonal equation , Journal of Computational Mathematics, v26 (2008), pp.336-346.
168. Y. Cheng, I.M. Gamba, A. Majorana and C.-W. Shu, Discontinuous Galerkin solver for Boltzmann-Poisson transients , Journal of Computational Electronics, v7 (2008), pp.119-123.
169. S. Zhang, S. Jiang and C.-W. Shu, Development of nonlinear weighted compact schemes with increasingly higher order accuracy , Journal of Computational Physics, v227 (2008), pp.7294-7321.
170. F. Li, C.-W. Shu, Y.-T. Zhang and H. Zhao, A second order discontinuous Galerkin fast sweeping method for Eikonal equations , Journal of Computational Physics, v227 (2008), pp.8191-8208.
171. J.-M. Qiu and C.-W. Shu, Convergence of high order finite volume weighted essentially non-oscillatory scheme and discontinuous Galerkin method for nonconvex conservation laws , SIAM Journal on Scientific Computing, v31 (2008), pp.584-607.
172. Y. Cheng and C.-W. Shu, Superconvergence and time evolution of discontinuous Galerkin finite element solutions , Journal of Computational Physics, v227 (2008), pp.9612-9627.
173. Y. Xu and C.-W. Shu, Local discontinuous Galerkin method for the Hunter-Saxton equation and its zero-viscosity and zero-dispersion limits , SIAM Journal on Scientific Computing, v31 (2008), pp.1249-1268.
174. C.-W. Shu, High order weighted essentially nonoscillatory schemes for convection dominated problems , SIAM Review, v51 (2009), pp.82-126.
175. Y.-T. Zhang and C.-W. Shu, Third order WENO scheme on three dimensional tetrahedral meshes , Communications in Computational Physics, v5 (2009), pp.836-848.
176. Y. Xia, Y. Xu and C.-W. Shu, Application of the local discontinuous Galerkin method for the Allen-Cahn/Cahn-Hilliard system , Communications in Computational Physics, v5 (2009), pp.821-835.
177. R. Abgrall and C.-W. Shu, Development of residual distribution schemes for the discontinuous Galerkin method: the scalar case with linear elements , Communications in Computational Physics, v5 (2009), pp.376-390.
178. L. Huang, S.C. Wong, M. Zhang, C.-W. Shu and W.H.K. Lam, Revisiting Hughes' dynamic continuum model for pedestrian flow and the development of an efficient solution algorithm , Transportation Research Part B, v43 (2009), pp.127-141.
179. W. Wang and C.-W. Shu, The WKB local discontinuous Galerkin method for the simulation of Schrodinger equation in a resonant tunneling diode , Journal of Scientific Computing, v40 (2009), pp.360-374.
180. S. Gottlieb, D.I. Ketcheson and C.-W. Shu, High order strong stability preserving time discretizations , Journal of Scientific Computing, v38 (2009), pp.251-289.
181. L. Huang, Y. Xia, S.C. Wong, C.-W. Shu, M. Zhang and W.H.K. Lam, Dynamic continuum model for bi-directional pedestrian flows , Proceedings of the Institution of Civil Engineers: Engineering and Computational Mechanics, v162 (2009), pp.67-75.
182. Y. Cheng and C.-W. Shu, Superconvergence of local discontinuous Galerkin methods for one-dimensional convection-diffusion equations , Computers and Structures, v87 (2009), pp.630-641.
183. Z. Xu, Y. Liu and C.-W. Shu, Hierarchical reconstruction for discontinuous Galerkin methods on unstructured grids with a WENO-type linear reconstruction and partial neighboring cells , Journal of Computational Physics, v228 (2009), pp.2194-2212.
184. Y. Xu and C.-W. Shu, Local discontinuous Galerkin method for surface diffusion and Willmore flow of graphs , Journal of Scientific Computing, v40 (2009), pp.375-390.
185. I. Roy, J.-M. Qiu, C.-W. Shu and L.-Z. Fang, A WENO algorithm for radiative transfer with resonant scattering and the Wouthuysen-field coupling , New Astronomy, v14 (2009), pp.513-520.
186. I. Roy, W. Xu, J.-M. Qiu, C.-W. Shu and L.-Z. Fang, Time evolution of Wouthuysen-field coupling , The Astrophysical Journal, v694 (2009), pp.1121-1130.
187. W. Chen, S.C. Wong, C.-W. Shu and P. Zhang, Front tracking algorithm for the Lighthill-Whitham-Richards traffic flow model with a piecewise quadratic, continuous, non-smooth, and non-concave fundamental diagram , International Journal of Numerical Analysis and Modeling, v6 (2009), pp.562-585.
188. Y. Lu, S.C. Wong, M. Zhang and C.-W. Shu, The entropy solutions for the Lighthill-Whitham-Richards traffic flow model with a discontinuous flow-density relationship , Transportation Science, v43 (2009), pp.511-530.
189. Y.-Y. Liu, C.-W. Shu and M.-P. Zhang, On the positivity of linear weights in WENO approximations , Acta Mathematicae Applicatae Sinica, English Series, v25 (2009), pp.503-538.
190. M. Zhang and C.-W. Shu, Fourier analysis for discontinuous Galerkin and related methods , Chinese Science Bulletin, v54 (2009), pp.1809-1816.
191. Z. Xu, Y. Liu and C.-W. Shu, Hierarchical reconstruction for spectral volume method on unstructured grids , Journal of Computational Physics, v228 (2009), pp.5787-5802.
192. W. Wang, C.-W. Shu, H.C. Yee and B. Sjogreen, High-order well-balanced schemes and applications to non-equilibrium flow , Journal of Computational Physics, v228 (2009), pp.6682-6702.
193. S. Zhang, S. Jiang, Y.-T. Zhang and C.-W. Shu, The mechanism of sound generation in the interaction between a shock wave and two counter-rotating vortices , Physics of Fluids, v21 (2009), 076101.
194. Y. Cheng, I.M. Gamba, A. Majorana and C.-W. Shu, A discontinuous Galerkin solver for Boltzmann-Poisson systems in nano devices , Computer Methods in Applied Mechanics and Engineering, v198 (2009), pp.3130-3150.
195. Y. Xia, S.C. Wong and C.-W. Shu, Dynamic continuum pedestrian flow model with memory effect , Physical Review E, v79 (2009), 066113.
196. S. Zhang, H. Zhang and C.-W. Shu, Topological structure of shock induced vortex breakdown , Journal of Fluid Mechanics, v639 (2009), pp.343-372.
197. I. Roy, W. Xu, J.-M. Qiu, C.-W. Shu and L.-Z. Fang, Wouthuysen-field coupling in 21 cm region around high-redshift sources , The Astrophysical Journal, v703 (2009), pp.1992-2003.
198. J. Cheng and C.-W. Shu, High order schemes for CFD: a review , Chinese Journal of Computational Physics, v26 (2009), pp.633-655.
199. B. Dong and C.-W. Shu, Analysis of a local discontinuous Galerkin method for linear time-dependent fourth-order problems , SIAM Journal on Numerical Analysis, v47 (2009), pp.3240-3268.
200. W. Liu, J. Cheng and C.-W. Shu, High order conservative Lagrangian schemes with Lax-Wendroff type time discretization for the compressible Euler equations , Journal of Computational Physics, v228 (2009), pp.8872-8891.
201. Y. Liu, C.-W. Shu and Z. Xu, Hierarchical reconstruction with up to second degree remainder for solving nonlinear conservation laws , Nonlinearity, v22 (2009), pp.2799-2812.
202. Y. Jiang, T. Xiong, S.C. Wong, C.-W. Shu, M. Zhang, P. Zhang and W.H.K. Lam, A reactive dynamic continuum user equilibrium model for bi-directional pedestrian flows , Acta Mathematica Scientia, v29B (2009), pp.1541-1555.
203. Y. Xu and C.-W. Shu, Local discontinuous Galerkin methods for high-order time-dependent partial differential equations , Communications in Computational Physics, v7 (2010), pp.1-46.
204. Y. Xu and C.-W. Shu, Dissipative numerical methods for the Hunter-Saxton equation , Journal of Computational Mathematics, v28 (2010), pp.606-620.
205. Y. Xia, Y. Xu and C.-W. Shu, Local discontinuous Galerkin methods for the generalized Zakharov system , Journal of Computational Physics, v229 (2010), pp.1238-1259.
206. Y. Cheng and C.-W. Shu, Superconvergence of discontinuous Galerkin and local discontinuous Galerkin schemes for linear hyperbolic and convection-diffusion equations in one space dimension , SIAM Journal on Numerical Analysis, v47 (2010), pp.4044-4072.
207. X. Zhang and C.-W. Shu, On maximum-principle-satisfying high order schemes for scalar conservation laws , Journal of Computational Physics, v229 (2010), pp.3091-3120.
208. T. Xiong, M. Zhang, Y.-T. Zhang and C.-W. Shu, Fast sweeping fifth order WENO scheme for static Hamilton-Jacobi equations with accurate boundary treatment , Journal of Scientific Computing, v45 (2010), pp.514-536.
209. X. Zhang and C.-W. Shu, A genuinely high order total variation diminishing scheme for one-dimensional scalar conservation laws , SIAM Journal on Numerical Analysis, v48 (2010), pp.772-795.
210. Q. Zhang and C.-W. Shu, Stability analysis and a priori error estimates of the third order explicit Runge-Kutta discontinuous Galerkin Method for scalar conservation laws , SIAM Journal on Numerical Analysis, v48 (2010), pp.1038-1063.
211. I. Roy, C.-W. Shu and L.-Z. Fang, Resonant scattering and Ly$\alpha$ radiation emergent from neutral hydrogen halos , The Astrophysical Journal, v716 (2010), pp.604-614.
212. Y. Liu and C.-W. Shu, Error analysis of the semi-discrete local discontinuous Galerkin method for semiconductor device simulation models , Science China Mathematics, v53 (2010), pp.3255-3278.
213. J. Cheng and C.-W. Shu, A cell-centered Lagrangian scheme with the preservation of symmetry and conservation properties for compressible fluid flows in two-dimensional cylindrical geometry , Journal of Computational Physics, v229 (2010), pp.7191-7206.
214. S. Tan and C.-W. Shu, Inverse Lax-Wendroff procedure for numerical boundary conditions of conservation laws , Journal of Computational Physics, v229 (2010), pp.8144-8166.
215. C. Wang and C.-W. Shu, An interface treating technique for compressible multi-medium flow with Runge-Kutta discontinuous Galerkin method , Journal of Computational Physics, v229 (2010), pp.8823-8843.
216. X. Zhang and C.-W. Shu, On positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations on rectangular meshes , Journal of Computational Physics, v229 (2010), pp.8918-8934.
217. Y. Xing, X. Zhang and C.-W. Shu, Positivity-preserving high order well-balanced discontinuous Galerkin methods for the shallow water equations , Advances in Water Resources, v33 (2010), pp.1476-1493.
218. W. Sun, S.C. Wong, P. Zhang and C.-W. Shu, A shock-fitting algorithm for the Lighthill-Whitham-Richards model on inhomogeneous highways , Transportmetrica, v7 (2011), pp.163-180.
219. R. Zhang, M. Zhang and C.-W. Shu, On the order of accuracy and numerical performance of two classes of finite volume WENO schemes , Communications in Computational Physics, v9 (2011), pp.807-827.
220. W. Wang, H.C. Yee, B. Sjogreen, T. Magin and C.-W. Shu, Construction of low dissipative high-order well-balanced filter schemes for non-equilibrium flows , Journal of Computational Physics, v230 (2011), pp.4316-4335.
221. W. Wang, J. Guzman and C.-W. Shu, The multiscale discontinuous Galerkin method for solving a class of second order elliptic problems with rough coefficients , International Journal of Numerical Analysis and Modeling, v8 (2011), pp.28-47.
222. J.-M. Qiu and C.-W. Shu, Conservative high order semi-Lagrangian finite difference WENO methods for advection in incompressible flow , Journal of Computational Physics, v230 (2011), pp.863-889.
223. Y. Xing, C.-W. Shu and S. Noelle, On the advantage of well-balanced schemes for moving-water equilibria of the shallow water equations , Journal of Scientific Computing, v48 (2011), pp.339-349.
224. T. Xiong, M. Zhang, C.-W. Shu, S.C. Wong and P. Zhang, High-order computational scheme for a dynamic continuum model for bi-directional pedestrian flow , Computer Aided Civil and Infrastructure Engineering, v26 (2011), pp.298-310.
225. Y. Xu and C.-W. Shu, Local discontinuous Galerkin methods for the Degasperis-Procesi equation , Communications in Computational Physics, v10 (2011), pp.474-508.
226. W. Liu, L. Yuan and C.-W. Shu, A conservative modification to the ghost fluid method for compressible multiphase flows , Communications in Computational Physics, v10 (2011), pp.785-806.
227. S. Zhang, S. Jiang and C.-W. Shu, Improvement of convergence to steady state solutions of Euler equations with the WENO schemes , Journal of Scientific Computing, v47 (2011), pp.216-238.
228. Y. Cheng, I.M. Gamba, A. Majorana and C.-W. Shu, A brief survey of the discontinuous Galerkin method for the Boltzmann-Poisson equations , SEMA Journal, v54 (2011), pp.47-64.
229. X. Zhang and C.-W. Shu, Positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations with source terms , Journal of Computational Physics, v230 (2011), pp.1238-1248.
230. J.-M. Qiu and C.-W. Shu, Conservative semi-Lagrangian finite difference WENO formulations with applications to the Vlasov equation , Communications in Computational Physics, v10 (2011), pp.979-1000.
231. X.-T. Shi, J. Chen, W.-T. Bi, C.-W. Shu and Z.-S. She, Numerical simulations of compressible mixing layers with a discontinuous Galerkin method , Acta Mechanica Sinica, v27 (2011), pp.318-329.
232. O. Bokanowski, Y. Cheng and C.-W. Shu, A discontinuous Galerkin solver for front propagation , SIAM Journal on Scientific Computing, v33 (2011), pp.923-938.
233. Y. Liu, C.-W. Shu and M. Zhang, High order finite difference WENO schemes for nonlinear degenerate parabolic equations , SIAM Journal on Scientific Computing, v33 (2011), pp.939-965.
234. Y. Liu, C.-W. Shu, E. Tadmor and M. Zhang, Central local discontinuous Galerkin methods on overlapping cells for diffusion equations , ESAIM: Mathematical Modelling and Numerical Analysis (M2AN), v45 (2011), pp.1009-1032.
235. X. Zhang and C.-W. Shu, Maximum-principle-satisfying and positivity-preserving high-order schemes for conservation laws: survey and new developments , Proceedings of the Royal Society A, v467 (2011), pp.2752-2776.
236. S. Tan and C.-W. Shu, A high order moving boundary treatment for compressible inviscid flows , Journal of Computational Physics, v230 (2011), pp.6023-6036.
237. R. Zhang, M. Zhang and C.-W. Shu, High order positivity-preserving finite volume WENO schemes for a hierarchical size-structured population model , Journal of Computational and Applied Mathematics, v236 (2011), pp.937-949.
238. Z. Xu, Y. Liu, H. Du, G. Lin and C.-W. Shu, Point-wise hierarchical reconstruction for discontinuous Galerkin and finite volume methods for solving conservation laws , Journal of Computational Physics, v230 (2011), pp.6843-6865.
239. X. Zhong and C.-W. Shu, Numerical resolution of discontinuous Galerkin methods for time dependent wave equations , Computer Methods in Applied Mechanics and Engineering, v200 (2011), pp.2814-2827.
240. Y. Xing and C.-W. Shu, High-order finite volume WENO schemes for the shallow water equations with dry states , Advances in Water Resources, v34 (2011), pp.1026-1038.
241. Y.-T. Zhang, S. Chen, F. Li, H. Zhao and C.-W. Shu, Uniformly accurate discontinuous Galerkin fast sweeping methods for Eikonal equations , SIAM Journal on Scientific Computing, v33 (2011), pp.1873-1896.
242. Y. Yang, I. Roy, C.-W. Shu and L.-Z. Fang, Effect of dust on Ly$\alpha$ photon transfer in optically thick halo , The Astrophysical Journal, v739 (2011), 91.
243. B. Ayuso, J.A. Carrillo and C.-W. Shu, Discontinuous Galerkin methods for the one-dimensional Vlasov-Poisson system , Kinetic and Related Models, v4 (2011), pp.955-989.
244. J.-M. Qiu and C.-W. Shu, Positivity preserving semi-Lagrangian discontinuous Galerkin formulation: theoretical analysis and application to the Vlasov-Poisson system , Journal of Computational Physics, v230 (2011), pp.8386-8409.
245. T. Xiong, P. Zhang, S.C. Wong, C.-W. Shu and M. Zhang, A macroscopic approach to the lane formation phenomenon in pedestrian counter flow , Chinese Physics Letters, v28 (2011), 108901.
246. Z. Xu, J. Xu and C.-W. Shu, A high order adaptive finite element method for solving nonlinear hyperbolic conservation laws , Journal of Computational Mathematics, v29 (2011), pp.491-500.
247. S. Zhang, S. Jiang, Q. Xu and C.-W. Shu, Numerical study of shock vortex interaction with high order finite difference WENO schemes , Computational Fluid Dynamics Journal, v18 (2011), pp.416-446.
248. C.-W. Shu, Efficient algorithms for solving partial differential equations with discontinuous solutions , Notices of the American Mathematical Society, v59 (2012), pp.615-621. Chinese translation in Mathematical Advances in Translation, v33 (2015), pp.307-314.
249. J. Cheng and C.-W. Shu Improvement on spherical symmetry in two-dimensional cylindrical coordinates for a class of control volume Lagrangian schemes , Communications in Computational Physics, v11 (2012), pp.1144-1168.
250. X. Zhang, Y. Xia and C.-W. Shu, Maximum-principle-satisfying and positivity-preserving high order discontinuous Galerkin schemes for conservation laws on triangular meshes , Journal of Scientific Computing, v50 (2012), pp.29-62.
251. W. Wang, C.-W. Shu, H.C. Yee and B. Sjogreen, High order finite difference methods with subcell resolution for advection equations with stiff source terms , Journal of Computational Physics, v231 (2012), pp.190-214.
252. X. Meng, C.-W. Shu and B. Wu, Superconvergence of the local discontinuous Galerkin method for linear fourth-order time-dependent problems in one space dimension , IMA Journal of Numerical Analysis, v32 (2012), pp.1294-1328.
253. C. Wang, X. Zhang, C.-W. Shu and J. Ning, Robust high order discontinuous Galerkin schemes for two-dimensional gaseous detonations , Journal of Computational Physics, v231 (2012), pp.653-665.
254. Y. Xu and C.-W. Shu, Optimal error estimates of the semi-discrete local discontinuous Galerkin methods for high order wave equations , SIAM Journal on Numerical Analysis, v50 (2012), pp.79-104.
255. X. Zhang and C.-W. Shu, A minimum entropy principle of high order schemes for gas dynamics equations , Numerische Mathematik, v121 (2012), pp.545-563.
256. X. Zhang and C.-W. Shu, Positivity-preserving high order finite difference WENO schemes for compressible Euler equations , Journal of Computational Physics, v231 (2012), pp.2245-2258.
257. S. Tan, C. Wang, C.-W. Shu and J. Ning, Efficient implementation of high order inverse Lax-Wendroff boundary treatment for conservation laws , Journal of Computational Physics, v231 (2012), pp.2510-2527.
258. X. Zhang, Y. Liu and C.-W. Shu, Maximum-principle-satisfying high order finite volume weighted essentially nonoscillatory schemes for convection-diffusion equations , SIAM Journal on Scientific Computing, v34 (2012), pp.A627-A658.
259. J. Cheng, C.-W. Shu and Q. Zeng, A conservative Lagrangian scheme for solving compressible fluid flows with multiple internal energy equations , Communications in Computational Physics, v12 (2012), pp.1307-1328.
260. T. Xiong, C.-W. Shu and M. Zhang, WENO scheme with subcell resolution for computing nonconservative Euler equations with applications to one-dimensional compressible two-medium flows , Journal of Scientific Computing, v53 (2012), pp.222-247.
261. B. Ayuso de Dios, J.A. Carrillo and C.-W. Shu, Discontinuous Galerkin methods for the multi-dimensional Vlasov-Poisson problem , Mathematical Models and Methods in Applied Sciences, v22 (2012), 1250042.
262. X. Meng, C.-W. Shu, Q. Zhang and B. Wu, Superconvergence of discontinuous Galerkin method for scalar nonlinear conservation laws in one space dimension , SIAM Journal on Numerical Analysis, v50 (2012), pp.2336-2356.
263. Y. Yang and C.-W. Shu, Analysis of optimal superconvergence of discontinuous Galerkin method for linear hyperbolic equations , SIAM Journal on Numerical Analysis, v50 (2012), pp.3110-3133.
264. C.-W. Shu, On high order accurate weighted essentially non-oscillatory and discontinuous Galerkin schemes for compressible turbulence simulations , Philosophical Transactions of the Royal Society A, v371 (2013), 20120172.
265. X. Zhong and C.-W. Shu, A simple weighted essentially nonoscillatory limiter for Runge-Kutta discontinuous Galerkin methods , Journal of Computational Physics, v232 (2013), pp.397-415.
266. Y. Xing and C.-W. Shu, High order well-balanced WENO scheme for the gas dynamics equations under gravitational fields , Journal of Scientific Computing, v54 (2013), pp.645-662.
267. S.-H. Zhang, X.-G. Deng, M.-L Mao and C.-W. Shu, Improvement of convergence to steady state solutions of Euler equations with weighted compact nonlinear schemes , Acta Mathematicae Applicatae Sinica, English Series, v29 (2013), pp.449-464.
268. Y. Zhang, X. Zhang and C.-W. Shu, Maximum-principle-satisfying second order discontinuous Galerkin schemes for convection-diffusion equations on triangular meshes , Journal of Computational Physics, v234 (2013), pp.295-316.
269. C. Wang, C.-W. Shu, W. Han and J. Ning, High resolution WENO simulation of 3D detonation waves , Combustion and Flame, v160 (2013), pp.447-462.
270. T. Xiong, C.-W. Shu and M. Zhang, A priori error estimates for semi-discrete discontinuous Galerkin methods solving nonlinear Hamilton-Jacobi equations with smooth solutions , International Journal of Numerical Analysis and Modeling, v10 (2013), pp.154-177.
271. Y. Yang and C.-W. Shu, Discontinuous Galerkin method for hyperbolic equations involving $\delta$-singularities: negative-order norm error estimates and applications , Numerische Mathematik, v124, (2013), pp.753-781.
272. Y. Jiang, C.-W. Shu and M. Zhang, An alternative formulation of finite difference weighted ENO schemes with Lax-Wendroff time discretization for conservation laws , SIAM Journal on Scientific Computing, v35 (2013), pp.A1137-A1160.
273. H.C. Yee, D.V. Kotov, W. Wang and C.-W. Shu, Spurious behavior of shock-capturing methods by the fractional step approach: problems containing stiff source terms and discontinuities , Journal of Computational Physics, v241 (2013), pp.266-291.
274. X.Y. Hu, N.A. Adams and C.-W. Shu, Positivity-preserving method for high-order conservative schemes solving compressible Euler equations , Journal of Computational Physics, v242 (2013), pp.169-180.
275. Y. Xing, C.-S. Chou and C.-W. Shu, Energy conserving local discontinuous Galerkin methods for wave propagation problems , Inverse Problems and Imaging, v7 (2013), pp.967-986.
276. X. Liu, S. Zhang, H. Zhang and C.-W. Shu, A new class of central compact schemes with spectral-like resolution I: Linear schemes , Journal of Computational Physics, v248 (2013), pp.235-256.
277. J. Zhu, X. Zhong, C.-W. Shu and J.-X. Qiu, Runge-Kutta discontinuous Galerkin method using a new type of WENO limiters on unstructured meshes , Journal of Computational Physics, v248 (2013), pp.200-220.
278. S. Zhang, H. Li, X. Liu, H. Zhang and C.-W. Shu, Classification and sound generation of two-dimensional interaction of two Taylor vortices , Physics of Fluids, v25 (2013), 056103.
279. W. Hao, J.D. Hauenstein, C.-W. Shu, A.J. Sommese, Z. Xu and Y.-T. Zhang, A homotopy method based on WENO schemes for solving steady state problems of hyperbolic conservation laws , Journal of Computational Physics, v250 (2013), pp.332-346.
280. Y. Yang, I. Roy, C.-W. Shu and L.-Z. Fang, Angular distribution of Ly$\alpha$ resonant photons emerging from optically thick medium , The Astrophysical Journal, v772 (2013), 3.
281. Y. Yang, D. Wei and C.-W. Shu, Discontinuous Galerkin method for Krause's consensus models and pressureless Euler equations , Journal of Computational Physics, v252 (2013), pp.109-127.
282. J. Du, S.C. Wong, C.-W. Shu, T. Xiong, M. Zhang and K. Choi, Revisiting Jiang's dynamic continuum model for urban cities , Transportation Research Part B, v56 (2013), pp.96-119.
283. J. Lu, C.-W. Shu and M. Zhang, Stability analysis and a priori error estimate of explicit Runge-Kutta discontinuous Galerkin methods for correlated random walk with density-dependent turning rates , Science China Mathematics, v56 (2013), pp.2645-2676.
284. C.-W. Shu, Bound-preserving high order accurate schemes , Notes of the Canadian Mathematical Society (CMS Notes), v45 (2013), pp.24-25.
285. W. Zhu, L.-L. Feng, Y. Xia, C.-W. Shu, Q. Gu and L.-Z. Fang, Turbulence in the intergalactic medium: solenoidal and dilatational motions and the impact of numerical viscosity , The Astrophysical Journal, v777 (2013), 48.
286. C.-W. Shu, A brief survey on discontinuous Galerkin methods in computational fluid dynamics , Advances in Mechanics, v43 (2013), pp.541-554.
287. Y. Jiang, C.-W. Shu and M. Zhang, Free-stream preserving finite difference schemes on curvilinear meshes , Methods and Applications of Analysis, v21 (2014), pp.1-30.
288. O. Bokanowski, Y. Cheng and C.-W. Shu, A discontinuous Galerkin scheme for front propagation with obstacles , Numerische Mathematik, v126 (2014), pp.1-31.
289. Q. Zhang and C.-W. Shu, Error estimates for the third order explicit Runge-Kutta discontinuous Galerkin method for linear hyperbolic equation in one-dimension with discontinuous initial data , Numerische Mathematik, v126 (2014), pp.703-740.
290. Z. Chen and C.-W. Shu, Recovering exponential accuracy from collocation point values of smooth functions with end-point singularities conservative schemes , Journal of Computational and Applied Mathematics, v265 (2014), pp.83-95.
291. J. Cheng and C.-W. Shu, Positivity-preserving Lagrangian scheme for multi-material compressible flow , Journal of Computational Physics, v257 (2014), pp.143-168.
292. Y. Zhang, W. Wang, J. Guzman and C.-W. Shu, Multi-scale discontinuous Galerkin method for solving elliptic problems with curvilinear unidirectional rough coefficients , Journal of Scientific Computing, v61 (2014), pp.42-60.
293. J. Niu, L. Zheng, Y. Yang and C.-W. Shu, Chebyshev spectral method for unsteady axisymmetric mixed convection heat transfer of power law fluid over a cylinder with variable transport properties , International Journal of Numerical Analysis and Modeling, v11 (2014), pp.525-540.
294. C.-S. Chou, C.-W. Shu and Y. Xing, Optimal energy conserving local discontinuous Galerkin methods for second-order wave equation in heterogeneous media , Journal of Computational Physics, v272 (2014), pp.88-107.
295. J. Cheng and C.-W. Shu, Second order symmetry-preserving conservative Lagrangian scheme for compressible Euler equations in two-dimensional cylindrical coordinates , Journal of Computational Physics, v272 (2014), pp.245-265.
296. Y. Xing and C.-W. Shu, A survey of high order schemes for the shallow water equations , Journal of Mathematical Study, v47 (2014), pp.221-249.
297. J. Du, C.-W. Shu and M. Zhang, A simple weighted essentially non-oscillatory limiter for the correction procedure via reconstruction (CPR) framework , Applied Numerical Mathematics, v95 (2015), pp.173-198.
298. F. Vilar and C.-W. Shu, Development and stability analysis of the inverse Lax-Wendroff boundary treatment for central compact schemes , ESAIM: Mathematical Modelling and Numerical Analysis ($M^{2}AN$), v49 (2015), pp.39-67.
299. W. Wang, C.-W. Shu, H.C. Yee, D.V. Kotov and B. Sj\"{o}green, High order finite difference methods with subcell resolution for stiff multispecies detonation capturing , Communications in Computational Physics, v17 (2015), pp.317-336.
300. H. Wang, C.-W. Shu and Q. Zhang, Stability and error estimates of local discontinuous Galerkin methods with implicit-explicit time-marching for advection-diffusion problems , SIAM Journal on Numerical Analysis, v53 (2015), pp.206-227.
301. X. Meng, C.-W. Shu and Y. Yang, Superconvergence of discontinuous Galerkin methods for time-dependent partial differential equations (in Chinese) , Scientia Sinica Mathematica, v45 (2015), pp.1041-1060.
302. J. Du, C.-W. Shu and M. Zhang, A simple weighted essentially non-oscillatory limiter for the correction procedure via reconstruction (CPR) framework on unstructured meshes , Applied Numerical Mathematics, v90 (2015), pp.146-167.
303. X. Liu, S. Zhang, H. Zhang and C.-W. Shu, A new class of central compact schemes with spectral-like resolution II: Hybrid weighted nonlinear schemes , Journal of Computational Physics, v284 (2015), pp.133-154.
304. C. Wang and C.-W. Shu, Progress on high-resolution numerical simulation of explosion mechanics , Chinese Science Bulletin (in Chinese), v60 (2015), pp.882-898.
305. J. Luo, C.-W. Shu and Q. Zhang, A priori error estimates to smooth solutions of the third order Runge-Kutta discontinuous Galerkin method for symmetrizable systems of conservation laws , ESAIM: Mathematical Modelling and Numerical Analysis ($M^{2}AN$), v49 (2015), pp.991-1018.
306. L. Wu and C.-W. Shu, Numerical solution of the viscous surface wave with discontinuous Galerkin method , ESAIM: Mathematical Modelling and Numerical Analysis ($M^{2}AN$), v49 (2015), pp.1019-1046.
307. Y. Jiang, C.-W. Shu and M. Zhang, High order finite difference WENO schemes with positivity-preserving limiter for correlated random walk with density-dependent turning rates , Mathematical Models and Methods in Applied Sciences ($M^3 AS$), v25 (2015), pp.1553-1588.
308. Y. Yang and C.-W. Shu, Analysis of sharp superconvergence of local discontinuous Galerkin method for one-dimensional linear parabolic equations , Journal of Computational Mathematics, v33 (2015), pp.323-340.
309. Z. Chen and C.-W. Shu, Recovering exponential accuracy in Fourier spectral methods involving piecewise smooth functions with unbounded derivative singularities , Journal of Scientific Computing, v65 (2015), pp.1145-1165.
310. W. Cao, C.-W. Shu, Y. Yang and Z. Zhang, Superconvergence of discontinuous Galerkin methods for 2-D hyperbolic equations , SIAM Journal on Numerical Analysis, v53 (2015), pp.1651-1671.
311. C. Wang, X. Dong and C.-W. Shu, Parallel adaptive mesh refinement method based on WENO finite difference scheme for the simulation of multi-dimensional detonation , Journal of Computational Physics, v298 (2015), pp.161-175.
312. J. Du, S.C. Wong, C.-W. Shu and M. Zhang, Reformulating the Hoogendoorn-Bovy predictive dynamic user-optimal model in continuum space with anisotropic condition , Transportation Research Part B, v79 (2015), pp.189-217.
313. X. Meng, C.-W. Shu and B. Wu, Optimal error estimates for discontinuous Galerkin methods based on upwind-biased fluxes for linear hyperbolic equations , Mathematics of Computation, v85 (2016), pp.1225-1261.
314. H. Wang, C.-W. Shu and Q. Zhang, Stability analysis and error estimates of local discontinuous Galerkin methods with implicit-explicit time-marching for nonlinear convection-diffusion problems , Applied Mathematics and Computation, v272 (2016), pp.237-258.
315. B. Dong, C.-W. Shu and W. Wang, A new multiscale discontinuous Galerkin method for the one-dimensional stationary Schr\"{o}dinger equation , Journal of Scientific Computing, v66 (2016), pp.321-345.
316. O. Bokanowski, Y. Cheng and C.-W. Shu, Convergence of discontinuous Galerkin schemes for front propagation with obstacles , Mathematics of Computation, v85 (2016), pp.2131-2159.
317. Y. Liu and C.-W. Shu, Analysis of the local discontinuous Galerkin method for the drift-diffusion model of semiconductor devices , Science China Mathematics, v59 (2016), pp.115-140.
318. J. Zhu, X. Zhong, C.-W. Shu and J.-X. Qiu, Runge-Kutta discontinuous Galerkin method with a simple and compact Hermite WENO limiter , Communications in Computational Physics, v19 (2016), pp.944-969.
319. H. Wang, S. Wang, C.-W. Shu and Q. Zhang, Local discontinuous Galerkin methods with implicit-explicit time-marching for multi-dimensional convection-diffusion problems , ESAIM: Mathematical Modelling and Numerical Analysis ($M^{2}AN$), v50 (2016), pp.1083-1105.
320. T. Li, C.-W. Shu and M. Zhang, Stability analysis of the inverse Lax-Wendroff boundary treatment for high order upwind-biased finite difference schemes , Journal of Computational and Applied Mathematics, v299 (2016), pp.140-158.
321. L. Wu, Y.-T. Zhang, S. Zhang and C.-W. Shu, High order fixed-point sweeping WENO methods for steady state of hyperbolic conservation laws and its convergence study , Communications in Computational Physics, v20 (2016), pp.835-869.
322. T. Qin, C.-W. Shu and Y. Yang, Bound-preserving discontinuous Galerkin methods for relativistic hydrodynamics , Journal of Computational Physics, v315 (2016), pp.323-347.
323. F. Vilar, C.-W. Shu and P.-H. Maire, Positivity-preserving cell-centered Lagrangian schemes for multi-material compressible flows: From first-order to high-orders. Part I: The one-dimensional case , Journal of Computational Physics, v312 (2016), pp.385-415.
324. F. Vilar, C.-W. Shu and P.-H. Maire, Positivity-preserving cell-centered Lagrangian schemes for multi-material compressible flows: From first-order to high-orders. Part II: The two-dimensional case , Journal of Computational Physics, v312 (2016), pp.416-442.
325. C.-W. Shu, High order WENO and DG methods for time-dependent convection-dominated PDEs: a brief survey of several recent developments , Journal of Computational Physics, v316 (2016), pp.598-613.
326. J. Lu, J. Fang, S. Tan, C.-W. Shu and M. Zhang, Inverse Lax-Wendroff procedure for numerical boundary conditions of convection-diffusion equations , Journal of Computational Physics, v317 (2016), pp.276-300.
327. J. Du and C.-W. Shu, A high order stable conservative method for solving hyperbolic conservation laws on arbitrarily distributed point clouds , SIAM Journal on Scientific Computing, v38 (2016), pp.A3094-A3128.
328. D. Yuan, J. Cheng and C.-W. Shu, High order positivity-preserving discontinuous Galerkin methods for radiative transfer equations , SIAM Journal on Scientific Computing, v38 (2016), pp.A2987-A3019.
329. C. Wang, J. Ding, C.-W. Shu and T. Li, Three-dimensional ghost-fluid large-scale numerical investigation on air explosion , Computers and Fluids, v137 (2016), pp.70-79.
330. D.S. Balsara, S. Garain and C.-W. Shu, An efficient class of WENO schemes with adaptive order , Journal of Computational Physics, v326 (2016), pp.780-804.
331. Z. Sun and C.-W. Shu, Stability analysis and error estimates of Lax-Wendroff discontinuous Galerkin methods for linear conservation laws , ESAIM: Mathematical Modelling and Numerical Analysis ($M^{2}AN$), v51 (2017), pp.1063-1087.
332. T. Li, C.-W. Shu and M. Zhang, Stability analysis of the inverse Lax-Wendroff boundary treatment for high order central difference schemes for diffusion equations , Journal of Scientific Computing, v70 (2017), pp.576-607.
333. J. Huang and C.-W. Shu, Error estimates to smooth solutions of semi-discrete discontinuous Galerkin methods with quadrature rules for scalar conservation laws , Numerical Methods for Partial Differential Equations, v33 (2017), pp.467-488.
334. J. Zhu, X. Zhong, C.-W. Shu and J. Qiu, Runge-Kutta discontinuous Galerkin method with a simple and compact Hermite WENO limiter on unstructured meshes , Communications in Computational Physics, v21 (2017), pp.623-649.
335. J. Guzman, C.-W. Shu and F.A. Sequeira, H(div) conforming and DG methods for incompressible Euler's equations , IMA Journal of Numerical Analysis, v37 (2017), pp.1733-1771.
336. H. Shen, C.-Y. Wen, M. Parsani and C.-W. Shu, Maximum-principle-satisfying space-time conservation element and solution element scheme applied to compressible multifluids , Journal of Computational Physics, v330 (2017), pp.668-692.
337. Z. Sun and C.-W. Shu, Stability of the fourth order Runge-Kutta method for time-dependent partial differential equations , Annals of Mathematical Sciences and Applications, v2 (2017), pp.255-284.
338. J. Huang and C.-W. Shu, A second-order asymptotic-preserving and positive-preserving discontinuous Galerkin scheme for the Kerr-Debye model , Mathematical Models and Methods in Applied Sciences, v27 (2017), pp.549–579.
339. X.H. Li, C.-W. Shu and Y. Yang, Local discontinuous Galerkin method for the Keller-Segel chemotaxis model , Journal of Scientific Computing, v73 (2017), pp.943-967.
340. G. Fu and C.-W. Shu, Analysis of an embedded discontinuous Galerkin method with implicit-explicit time-marching for convection-diffusion problems , International Journal of Numerical Analysis and Modeling, v14 (2017), pp.477-499.
341. C.Y. Lam and C.-W. Shu, A phase-based interior penalty discontinuous Galerkin method for the Helmholtz equation with spatially varying wavenumber , Computer Methods in Applied Mechanics and Engineering, v318 (2017), pp.456-473.
342. F. Zheng, C.-W. Shu and J. Qiu, Finite difference Hermite WENO schemes for the Hamilton-Jacobi equations , Journal of Computational Physics, v337 (2017), pp.27-41.
343. J. Li, C. Shi and C.-W. Shu, Optimal non-dissipative discontinuous Galerkin methods for Maxwell's equations in Drude metamaterials , Computers and Mathematics with Applications, v73 (2017), pp.1760-1780.
344. Y. Liu, Y. Cheng and C.-W. Shu, A simple bound-preserving sweeping technique for conservative numerical approximations , Journal of Scientific Computing, v73 (2017), pp.1028-1071.
345. H. Wang, Q. Zhang and C.-W. Shu, Stability analysis and error estimates of local discontinuous Galerkin methods with implicit-explicit time-marching for the time-dependent fourth order PDEs , ESAIM: Mathematical Modelling and Numerical Analysis ($M^{2}AN$), v51 (2017), pp.1931-1955.
346. Q. Liu, C.-W. Shu and M. Zhang, Discontinuous Galerkin methods for weakly coupled hyperbolic multi-domain problems , SIAM Journal on Scientific Computing, v321 (2017), pp.209-234.
347. J. Morales-Escalante, I.M. Gamba, Y. Cheng, A. Majorana, C.-W. Shu and J. Chelikowsky, Discontinuous Galerkin deterministic solvers for a Boltzmann-Poisson model of hot electron transport byaveraged empirical pseudopotential band structures , Computer Methods in Applied Mechanics and Engineering, v321 (2017), pp.209-234.
348. W. Cao, C.-W. Shu and Z. Zhang, Superconvergence of discontinuous Galerkin methods for 1-D linear hyperbolic equations with degenerate variable coefficients , ESAIM: Mathematical Modelling and Numerical Analysis ($M^{2}AN$), v51 (2017), pp.2213-2235.
349. T. Chen and C.-W. Shu, Entropy stable high order discontinuous Galerkin methods with suitable quadrature rules for hyperbolic conservation laws , Journal of Computational Physics, v345 (2017), pp.427-461.
350. G. Fu and C.-W. Shu, A new trouble-cell indicator for discontinuous Galerkin methods for hyperbolic conservation laws , Journal of Computational Physics, v347 (2017), pp.305-327.
351. H. Song and C.-W. Shu, Unconditional energy stability analysis of a second order implicit-explicit local discontinuous Galerkin method for the Cahn-Hilliard equation , Journal of Scientific Computing, v73 (2017), pp.1178-1203.
352. J. Zhu and C.-W. Shu, Numerical study on the convergence to steady state solutions of a new class of high order WENO schemes , Journal of Computational Physics, v349 (2017), pp.80-96.
353. D. Ling, J. Cheng and C.-W. Shu, Positivity-preserving and symmetry-preserving Lagrangian schemes for compressible Euler equations in cylindrical coordinates, , Computers and Fluids, v157 (2017), pp.112-130.
354. J. Du and C.-W. Shu, Positivity-preserving high-order schemes for conservation laws on arbitrarily distributed point clouds with a simple WENO limiter , International Journal of Numerical Analysis and Modeling, v15 (2018), pp.1-25.
355. C. Shi and C.-W. Shu, ` On local conservation of numerical methods for conservation laws , Computers and Fluids, v169 (2018), pp.3-9.
356. Z. Sun, J.A. Carrillo and C.-W. Shu, A discontinuous Galerkin method for nonlinear parabolic equations and gradient flow problems with interaction potentials , Journal of Computational Physics, v352 (2018), pp.76-104.
357. T. Qin and C.-W. Shu, Implicit positivity-preserving high order discontinuous Galerkin methods for conservation laws , SIAM Journal on Scientific Computing, v40 (2018), pp.A81-A107.
358. Y. Liu, C.-W. Shu and M. Zhang, Entropy stable high order discontinuous Galerkin methods for ideal compressible MHD on structured meshes , Journal of Computational Physics, v354 (2018), pp.163-178.
359. Y. Liu, C.-W. Shu and M. Zhang, Optimal error estimates of the semidiscrete central discontinuous Galerkin methods for linear hyperbolic equations , SIAM Journal on Numerical Analysis, v56 (2018), pp.520-541.
360. W. Cao, C.-W. Shu, Y. Yang and Z. Zhang, Superconvergence of discontinuous Galerkin method for scalar nonlinear hyperbolic equations potentials , SIAM Journal on Numerical Analysis, v56 (2018), pp.732-765.
361. F. Filbet and C.-W. Shu, Discontinuous-Galerkin methods for a kinetic model of self-organized dynamics potentials , Mathematical Models and Methods in Applied Sciences ($M^3 AS$), v28 (2018), pp.1171-1197.
362. J. Huang and C.-W. Shu, Bound-preserving modified exponential Runge-Kutta discontinuous Galerkin methods for scalar hyperbolic equations with stiff source terms , Journal of Computational Physics, v361 (2018), pp.111-135.
363. D. Ling, J. Cheng and C.-W. Shu, Conservative high order positivity-preserving discontinuous Galerkin methods for linear hyperbolic and radiative transfer equations , Journal of Scientific Computing, v77 (2018), pp.1801-1831.
364. H. Wang, Q. Zhang and C.-W. Shu, Third order implicit-explicit Runge-Kutta local discontinuous Galerkin methods with suitable boundary treatment for convection-diffusion problems with Dirichlet boundary conditions , Journal of Computational and Applied Mathematics, v342 (2018), pp.164-179.
365. C. Shi, J. Li and C.-W. Shu, Discontinuous Galerkin methods for Maxwell's equations in Drude metamaterials on unstructured meshes , Journal of Computational and Applied Mathematics, v342 (2018), pp.147-163.
366. K. Wu and C.-W. Shu, A provably positive discontinuous Galerkin method for multidimensional ideal magnetohydrodynamics , SIAM Journal on Scientific Computing, v40 (2018), pp.B1302-B1329.
367. J. Zhu and C.-W. Shu, A new type of multi-resolution WENO schemes with increasingly higher order of accuracy , Journal of Computational Physics, v375 (2018), pp.659-683.
368. H. Wang, Y. Liu, Q. Zhang and C.-W. Shu, Local discontinuous Galerkin methods with implicit-explicit time-marching for time-dependent incompressible fluid flow , Mathematics of Computation, v88 (2019), pp.91-121.
369. V. Kucera and C.-W. Shu, On the time growth of the error of the DG method for advective problems , IMA Journal of Numerical Analysis, v39 (2019), pp.687-712.
370. J. Zhu and C.-W. Shu, Numerical study on the convergence to steady state solutions of a new class of finite volume WENO schemes: triangular meshes , Shock Waves, v29 (2019), pp.3-25.
371. T. Chen, B. Rozovskii and C.-W. Shu, Numerical solutions of stochastic PDEs driven by arbitrary type of noise , Stochastics and Partial Differential Equations: Analysis and Computations, v7 (2019), pp.1-39.
372. L. Yang, T. Li, S.C. Wong, C.-W. Shu and M. Zhang, Modeling and simulation of urban air pollution from the dispersion of vehicle exhaust: a continuum modeling approach , International Journal of Sustainable Transportation, v13 (2019), pp.722-740.
373. J. Huang and C.-W. Shu, Positivity-preserving time discretizations for production-destruction equations with applications to non-equilibrium flows , Journal of Scientific Computing, v78 (2019), pp.1811-1839.
374. G. Fu and C.-W. Shu, Optimal energy-conserving discontinuous Galerkin methods for linear symmetric hyperbolic systems , Journal of Computational Physics, v394 (2019), pp.329-363.
375. G. Fu and C.-W. Shu, An energy-conserving ultra-weak discontinuous Galerkin method for the generalized Korteweg-De Vries equation , Journal of Computational and Applied Mathematics, v349 (2019), pp.41-51.
376. Y. Liu, Q. Liu, Y. Liu, C.-W. Shu and M. Zhang, Locally divergence-free spectral-DG methods for ideal magnetohydrodynamic equations on cylindrical coordinates , Communications in Computational Physics, v26 (2019), pp.631-653.
377. L. Zhou, Y. Xia and C.-W. Shu, Stability analysis and error estimates of arbitrary Lagrangian-Eulerian discontinuous Galerkin method coupled with Runge-Kutta time-marching for linear conservation laws , ESAIM: Mathematical Modelling and Numerical Analysis ($M^{2}AN$), v53 (2019), pp.105-144.
378. J. Huang, W. Zhao and C.-W. Shu, A third-order unconditionally positivity-preserving scheme for production-destruction equations with applications to non-equilibrium flows , Journal of Scientific Computing, v79 (2019), pp.1015-1056.
379. Y. Liu, C.-W. Shu and M. Zhang, Superconvergence of energy-conserving discontinuous Galerkin methods for linear hyperbolic equations , Communications on Applied Mathematics and Computation, v1 (2019), pp.101-116.
380. F. Zheng, C.-W. Shu and J. Qiu, High order finite difference Hermite WENO schemes for the Hamilton-Jacobi equations on unstructured meshes , Computers and Fluids, v183 (2019), pp.53-65.
381. Z. Sun, J.A. Carrillo and C.-W. Shu, An entropy stable high-order discontinuous Galerkin method for cross-diffusion gradient flow systems , Kinetic and Related Models, v12 (2019), pp.885-908.
382. K. Wu and C.-W. Shu, Provably positive high-order schemes for ideal magnetohydrodynamics: analysis on general meshes , Numerische Mathematik, v142 (2019), pp.995-1047.
383. Z. Sun and C.-W. Shu, Strong stability of explicit Runge-Kutta time discretizations , SIAM Journal on Numerical Analysis, v57 (2019), pp.1158-1182.
384. S. Amat, J. Ruiz and C.-W. Shu, On new strategies to control the accuracy of WENO algorithms close to discontinuities , SIAM Journal on Numerical Analysis, v57 (2019), pp.1205-1237.
385. J. Zhu and C.-W. Shu, A new type of multi-resolution WENO schemes with increasingly higher order of accuracy on triangular meshes , Journal of Computational Physics, v392 (2019), pp.19-33.
386. Y. Xu, Q. Zhang, C.-W. Shu and H. Wang, The L$^2$-norm stability analysis of Runge-Kutta discontinuous Galerkin methods for linear hyperbolic equations , SIAM Journal on Numerical Analysis, v57 (2019), pp.1574-1601.
387. Y. Li, J. Cheng, Y. Xia and C.-W. Shu, High order arbitrary Lagrangian-Eulerian finite difference WENO scheme for Hamilton-Jacobi equations , Communications in Computational Physics, v26 (2019), pp.1530-1574.
388. Y. Liu, T. Chen, Y. Chen and C.-W. Shu, Certified offline-free reduced basis (COFRB) methods for stochastic differential equations driven by arbitrary types of noise , Journal of Scientific Computing, v81 (2019), pp.1210-1239.
389. A. Mazaheri, C.-W. Shu and V. Perrier, Bounded and compact weighted essentially nonoscillatory limiters for discontinuous Galerkin schemes: triangular elements , Journal of Computational Physics, v395 (2019), pp.461-488.
390. S. Zhang, J. Zhu and C.-W. Shu, A brief review on the convergence to steady state solutions of Euler equations with high-order WENO schemes , Advances in Aerodynamics, v1 (2019), article number 16.
391. Z. Cheng, J. Fang, C.-W. Shu and M. Zhang, Assessment of aeroacoustic resolution properties of DG schemes and comparison with DRP schemes , Journal of Computational Physics, v399 (2019), 108960.
392. H. Wang, Q. Zhang and C.-W. Shu, Implicit-explicit local discontinuous Galerkin methods with generalized alternating numerical fluxes for convection-diffusion problems , Journal of Scientific Computing, v81 (2019), pp.2080-2114.
393. H. Wang, Q. Zhang, S. Wang and C.-W. Shu, Local discontinuous Galerkin methods with explicit-implicit-null time discretizations for solving nonlinear diffusion problems , Science China Mathematics, v63 (2020), pp.183-204.
394. N.D.P. da Silva, C.H. Marchi, L.K. Araki, R.B. de R. Borges, G. Bertoldo and C.-W. Shu, Completed repeated Richardson extrapolation for compressible fluid flows , Applied Mathematical Modelling, v77 (2020), pp.724-737.
395. J. Zhu and C.-W. Shu, Convergence to steady-state solutions of the new type of high-order multi-resolution WENO schemes: a numerical study , Communications on Applied Mathematics and Computation, v2 (2020), pp.429-460.
396. Y. Li, C.-W. Shu and S. Tang, A discontinuous Galerkin method for stochastic conservation laws , SIAM Journal on Scientific Computing, v42 (2020), pp.A54-A86.
397. J. Zhu, J. Qiu and C.-W. Shu, High-order Runge-Kutta discontinuous Galerkin methods with a new type of multi-resolution WENO limiters , Journal of Computational Physics, v404 (2020), 109105.
398. Y. Liu, C.-W. Shu and M. Zhang, Optimal error estimates of the semidiscrete discontinuous Galerkin methods for two dimensional hyperbolic equations on Cartesian meshes using $P^k$ elements , ESAIM: Mathematical Modelling and Numerical Analysis (ESAIM: $M^{2}AN$), v54 (2020), pp.705-726.
399. J. Zhu and C.-W. Shu, A new type of third-order finite volume multi-resolution WENO schemes on tetrahedral meshes , Journal of Computational Physics, v406 (2020), 109212.
400. J.A. Carrillo, S. Kalliadasis, S.P. Perez and C.-W. Shu, Well-balanced finite volume schemes for hydrodynamic equations with general free energy , Multiscale Modeling and Simulation, v18 (2020), pp.502-541.
401. Y. Li, C.-W. Shu and S. Tang, An ultra-weak DG method with IMEX time-marching for generalized stochastic KdV equations , Journal of Scientific Computing, v82 (2020), 61.
402. S. Amat, J. Ruiz and C.-W. Shu, On a new WENO algorithm of order $2r$ with improved accuracy close to discontinuities , Applied Mathematics Letters, v105 (2020), 106298.
403. J. Zhu, C.-W. Shu and J. Qiu, High-order Runge-Kutta discontinuous Galerkin methods with a new type of multi-resolution WENO limiters on triangular meshes , Applied Numerical Mathematics, v153 (2020), pp.519-539.
404. Y. Liu, Q. Tao and C.-W. Shu, Analysis of optimal superconvergence of an ultraweak-local discontinuous Galerkin method for a time dependent fourth-order equation , ESAIM: Mathematical Modelling and Numerical Analysis ($M^{2}AN$), v54 (2020), pp.1797-1820.
405. T. Chen and C.-W. Shu, Review of entropy stable discontinuous Galerkin methods for systems of conservation laws on unstructured simplex meshes , CSIAM Transactions on Applied Mathematics (CSAM), v1 (2020), pp.1-52.
406. K. Wu and C.-W. Shu, Entropy symmetrization and high-order accurate entropy stable numerical schemes for relativistic MHD equations , SIAM Journal on Scientific Computing, v42 (2020), pp.A2230-A2261.
407. S. Ding, C.-W. Shu and M. Zhang, On the conservation of finite difference WENO schemes in non-rectangular domains using the inverse Lax-Wendroff boundary treatments , Journal of Computational Physics, v415 (2020), 109516.
408. Y. Li, J. Cheng, Y. Xia and C.-W. Shu, On moving mesh WENO schemes with characteristic boundary conditions for Hamilton-Jacobi equations , Computers and Fluids, v205 (2020), 104582.
409. Q. Tao, Y. Xu and C.-W. Shu, An ultraweak-local discontinuous Galerkin method for PDEs with high order spatial derivatives , Mathematics of Computation, v89 (2020), pp.2753-2783.
410. Y. Xu, X. Meng, C.-W. Shu and Q. Zhang, Superconvergence analysis of the Runge-Kutta discontinuous Galerkin methods for a linear hyperbolic equation , Journal of Scientific Computing, v84 (2020), 23.
411. J. Cheng, C.-W. Shu and P. Song, High order conservative Lagrangian schemes for one-dimensional radiative hydrodynamics equations in the equilibrium limit , Journal of Computational Physics, v421 (2020), 109724.
412. Y. Xu, C.-W. Shu and Q. Zhang, Error estimate of the fourth order Runge-Kutta discontinuous Galerkin methods for linear hyperbolic equations, , SIAM Journal on Numerical Analysis, v58 (2020), pp.2885-2914.
413. H. Fan and C.-W. Shu, Existence and computation of solutions of a model of traffic involving hysteresis , SIAM Journal on Applied Mathematics, v80 (2020), pp.2319-2337.
414. J. Cheng and C.-W. Shu, High order Lagrangian schemes and their positivity-preserving property for compressible fluid flow , Mathematica Numerica Sinica (in Chinese), v42 (2020), pp.261-278.
415. C.-W. Shu, Essentially non-oscillatory and weighted essentially non-oscillatory schemes , Acta Numerica, v29 (2020), pp.701-762.
416. S. Amat, J. Ruiz, C.-W. Shu and D.F. Yanez, A new WENO-2r algorithm with progressive order of accuracy close to discontinuities , SIAM Journal on Numerical Analysis, v58 (2020), pp.3448-3474.
417. S. Amat, J. Ruiz and C.-W. Shu, On new strategies to control the accuracy of WENO algorithm close to discontinuities II: Cell averages and multiresolution , Journal of Computational Mathematics, v38 (2020), pp.661-682.
418. Y. Liu, C.-W. Shu and M. Zhang, Sub-optimal convergence of discontinuous Galerkin methods with central fluxes for linear hyperbolic equations with even degree polynomial approximations , Journal of Computational Mathematics, v39 (2021), pp.629-648.
419. S. Amat, J. Ruiz, C.-W. Shu and J.C. Trillo, On a class of splines free of Gibbs phenomenon , ESAIM: Mathematical Modelling and Numerical Analysis ($M^{2}AN$), v55 (2021), pp.S29-S64.
420. Y. Li, C.-W. Shu and S. Tang, A local discontinuous Galerkin method for nonlinear parabolic SPDEs , ESAIM: Mathematical Modelling and Numerical Analysis ($M^{2}AN$), v55 (2021), pp.S187-S223.
421. R.B. de R. Borges, N.D.P. da Silva, F.A.A. Gomes, C.-W. Shu and S. Tan, A sequel of the inverse Lax--Wendroff high order wall boundary treatment for conservation laws , Archives of Computational Methods in Engineering, v28 (2021), pp.2315-2329.
422. S. Amat, J. Ruiz, A. Baeza and C.-W. Shu, On a new centered strategy to control the accuracy of weighted essentially non oscillatory algorithm for conservation laws close to discontinuities , Numerical Methods for Partial Differential Equations, v37 (2021), pp.172-195.
423. Y. Liu, J. Lu, C.-W. Shu and M. Zhang, Central discontinuous Galerkin methods on overlapping meshes for wave equations , Mathematical Modelling and Numerical Analysis ($M^{2}AN$), v55 (2021), pp.329-356.
424. Q. Tao, Y. Xu and C.-W. Shu, A discontinuous Galerkin method and its error estimate for nonlinear fourth-order wave equations , Journal of Computational and Applied Mathematics, v386 (2021), 113230.
425. N. Lei, J. Cheng and C.-W. Shu, A high order positivity-preserving conservative WENO remapping method on 2D quadrilateral meshes , Computer Methods in Applied Mechanics and Engineering, v373 (2021), 113497.
426. J. Lu, C.-W. Shu, S. Tan and M. Zhang, An inverse Lax-Wendroff procedure for hyperbolic conservation laws with changing wind direction on the boundary , Journal of Computational Physics, v426 (2021), 109940.
427. Z. Sun and C.-W. Shu, Enforcing strong stability of explicit Runge-Kutta methods with superviscosity , Communications on Applied Mathematics and Computation, v3 (2021), pp.671-700.
428. Y.-L. Liu, C.-W. Shu and A.-M. Zhang, Weighted ghost fluid discontinuous Galerkin method for two-medium problems , Journal of Computational Physics, v426 (2021), 109956.
429. J. Zhu, C.-W. Shu and J. Qiu, High-order Runge-Kutta discontinuous Galerkin methods with a new type of multi-resolution WENO limiters on tetrahedral meshes , Communications in Computational Physics, v29 (2021), pp.1030-1058.
430. Q. Zhang, Y. Xu and C.-W. Shu, Dissipative and conservative local discontinuous Galerkin methods for the Fornberg-Whitham type equations , Communications in Computational Physics, v30 (2021), pp.321-356.
431. M. Tan, J. Cheng and C.-W. Shu, Stability of high order finite difference schemes with implicit-explicit time-marching for convection-diffusion and convection-dispersion equations , International Journal of Numerical Analysis and Modeling, v18 (2021), pp.362-383.
432. S. Amat, J. Ruiz-Alvarez, C.-W. Shu and D.F. Yanez, Cell-average WENO with progressive order of accuracy close to discontinuities with applications to signal processing , Applied Mathematics and Computation, v403 (2021), 126131.
433. J. Lu, Y. Liu and C.-W. Shu, An oscillation-free discontinuous Galerkin method for scalar hyperbolic conservation laws , SIAM Journal on Numerical Analysis, v59 (2021), pp.1299-1324.
434. J. Zhu, C.-W. Shu and J. Qiu, High-order Runge-Kutta discontinuous Galerkin methods with multi-resolution WENO limiters for solving steady-state problems , Applied Numerical Mathematics, v165 (2021), pp.482-499.
435. K. Wu and C.-W. Shu, Provably physical-constraint-preserving discontinuous Galerkin methods for multidimensional relativistic MHD equations , Numerische Mathematik, v148 (2021), pp.699-741.
436. F. Zheng, C.-W. Shu and J. Qiu, A high order conservative finite difference scheme for compressible two-medium flows , Journal of Computational Physics, v445 (2021), 110597.
437. J. Li, C.-W. Shu and J. Qiu, Multi-resolution HWENO schemes for hyperbolic conservation laws , Journal of Computational Physics, v446 (2021), 110653.
438. T. Li, J. Lu and C.-W. Shu, Stability analysis of inverse Lax-Wendroff boundary treatment ofhigh order compact difference schemes for parabolic equations , Journal of Computational and Applied Mathematics, v400 (2022), 113711.
439. X. Yu and C.-W. Shu, Multi-layer perceptron estimator for the total variation bounded constant in limiters for discontinuous Galerkin methods , La Matematica: Official Journal of the Association for Women in Mathematics, v1 (2022), pp.53-84.
440. Y. Liu, J. Lu and C.-W. Shu, An essentially oscillation-free discontinuous Galerkin method for hyperbolic systems , SIAM Journal on Scientific Computing, v44 (2022), pp.A230-A259.
441. R.B. de R. Borges, N.D.P. da Silva, F.A.A. Gomes and C.-W. Shu, High-resolution viscous terms discretization and ILW solid wall boundary treatment for the Navier-Stokes equations , Archives of Computational Methods in Engineering, v29 (2022), pp.2383-2395.
442. L. Yang, S.C. Wong, H.W. Ho, M. Zhang and C.-W. Shu, Effects of air quality on housing location: A predictive dynamic continuum user-optimal approach , Transportation Science, v56 (2022), pp.1111-1134.
443. N. Lei, J. Cheng and C.-W. Shu, High order entropy stable and positivity-preserving discontinuous Galerkin method for the nonlocal electron heat transport model , Journal of Computational Physics, v454 (2022), 110945.
444. J. Li, C.-W. Shu and W. Yang, Development and analysis of two new finite element schemes for a time-domain carpet cloak model , Advances in Computational Mathematics, v48 (2022), 24.
445. X. Yu, J. Li and C.-W. Shu, Local discontinuous Galerkin methods for the carpet cloak model , Annals of Mathematical Sciences and Applications, v7 (2022), pp.97-137.
446. X. Zhong and C.-W. Shu, Entropy stable Galerkin methods with suitable quadrature rules for hyperbolic systems with random inputs , Journal of Scientific Computing, v92 (2022), 14.
447. J. Sun, C.-W. Shu and Y. Xing, Multi-symplectic discontinuous Galerkin methods for the stochastic Maxwell equations with additive noise , Journal of Computational Physics, v461 (2022), 111199.
448. M. Jiao, Y. Jiang, C.-W. Shu and M. Zhang, Optimal error estimates to smooth solutions of the central discontinuous Galerkin methods for nonlinear scalar conservation laws , ESAIM: Mathematical Modelling and Numerical Analysis ($M^{2}AN$), v56 (2022), pp.1401-1435.
449. N. Lei, J. Cheng and C.-W. Shu, A high order positivity-preserving conservative WENO remapping method on 3D tetrahedral meshes , Computer Methods in Applied Mechanics and Engineering, v395 (2022), 115037.
450. C.-W. Shu, Inverse Lax-Wendroff boundary treatment: a survey , Communications in Mathematical Research, v38 (2022), pp.333-350.
451. J. Ai, Y. Xu, C.-W. Shu and Q. Zhang, L$^2$ error estimate to smooth solutions of high order Runge--Kutta discontinuous Galerkin method for scalar nonlinear conservation laws with and without sonic points , SIAM Journal on Numerical Analysis, v60 (2022), pp.1741-1773.
452. L.K. Araki, R.B. de R. Borges, N.D.P. da Silva and C.-W. Shu, High-resolution ILW outflow boundary treatment for the Navier-Stokes equations , Computers and Fluids, v242 (2022), 105506.
453. M. Tan, J. Cheng and C.-W. Shu, Stability of high order finite difference and local discontinuous Galerkin schemes with explicit-implicit-null time-marching for high order dissipative and dispersive equations , Journal of Computational Physics, v464 (2022), 111314.
454. J. Li, C.-W. Shu and J. Qiu, Moment-based multi-resolution HWENO scheme for hyperbolic conservation laws , Communications in Computational Physics, v32 (2022), pp.364-400.
455. Z. Xu and C.-W. Shu, High order conservative positivity-preserving discontinuous Galerkin method for stationary hyperbolic equations , Journal of Computational Physics, v466 (2022), 111410.
456. J. Du, C.-W. Shu and X. Zhong, An improved simple WENO limiter for discontinuous Galerkin methods solving hyperbolic systems on unstructured meshes , Journal of Computational Physics, v467 (2022), 111424.
457. S. Amat, J. Ruiz-Alvarez, C.-W. Shu and D.F. Yanez, On the approximation of derivative values using a WENO algorithm with progressive order of accuracy close to discontinuities , Computational and Applied Mathematics, v41 (2022), 297.
458. Z. Xu and C.-W. Shu, Third order maximum-principle-satisfying and positivity-preserving Lax-Wendroff discontinuous Galerkin methods for hyperbolic conservation laws , Journal of Computational Physics, v470 (2022), 111591.
459. L. Li, J. Zhu, C.-W. Shu and Y.-T. Zhang, A fixed-point fast sweeping WENO method with inverse Lax-Wendroff boundary treatment for steady state of hyperbolic conservation laws , Communications on Applied Mathematics and Computation, v5 (2023), pp.403-427.
460. D. Ling, C.-W. Shu and W. Yan, Local discontinuous Galerkin methods for diffusive-viscous wave equations , Journal of Computational and Applied Mathematics, v419 (2023), 114690.
461. K. Wu and C.-W. Shu, Geometric quasilinearization for analysis and design of bound-preserving schemes , SIAM Review, v65 (2023), pp.1031-1073.
462. K. Wu, H. Jiang and C.-W. Shu, Provably positive central DG schemes via geometric quasolinearization for ideal MHD equations , SIAM Journal on Numerical Analysis, v61 (2023), pp.250-285.
463. S. Liu, S. Osher, W. Li and C.-W. Shu, A primal-dual approach for solving conservation laws with implicit in time approximations , Journal of Computational Physics, v472 (2023), 111654.
464. J. Sun, C.-W. Shu and Y. Xing, Discontinuous Galerkin methods for stochastic Maxwell equations with multiplicative noise , ESAIM: Mathematical Modelling and Numerical Analysis ($M^{2}AN$), v57 (2023), pp.841-864.
465. H. Fan and C.-W. Shu, High order numerical methods for flows with hysteretic fluxes , Applied Numerical Mathematics, v184 (2023), pp.234-252.
466. S. Liu, Y. Jiang, C.-W. Shu, M. Zhang and S. Zhang, A high order moving boundary treatment for convection-diffusion equations , Journal of Computational Physics, v473 (2023), 111752.
467. X. Gu, Y. Li, J. Cheng and C.-W. Shu, A high order positivity-preserving conservative WENO remapping method based on a moving mesh solver , Journal of Computational Physics, v473 (2023), 111754.
468. L. Yang, C.-W. Shu, S.C. Wong, M. Zhang and J. Du, On the existence and uniqueness properties of the Hoogendoorn-Bovy pedestrian flow model , Transportmetrica B: Transport Dynamics, v11 (2023), pp.912-937.
469. N. Lei, J. Cheng and C.-W. Shu, A high order positivity-preserving polynomial projection remapping method , Journal of Computational Physics, v474 (2023), 111826.
470. J. Huang, T. Izgin, S. Kopecz, A. Meister and C.-W. Shu, On the stability of strong-stability-preserving modified Patankar Runge-Kutta schemes , ESAIM: Mathematical Modelling and Numerical Analysis ($M^{2}AN$), v57 (2023), pp.1063-1086.
471. M. Tan, J. Cheng and C.-W. Shu, Stability of spectral collocation schemes with explicit-implicit-null time-marching for convection-diffusion and convection-dispersion equations , East Asian Journal on Applied Mathematics, v13 (2023), pp.464-498.
472. H. Wang, F. Li, C.-W. Shu and Q. Zhang, Uniform stability for local discontinuous Galerkin methods with implicit-explicit Runge-Kutta time discretizations for linear convection-diffusion equation , Mathematics of Computation, v92 (2023), pp.2475-2513.
473. L. Yang, S.C. Wong, H.W. Ho, C.-W. Shu and M. Zhang, Bi-level optimization of the housing allocation and traffic emission problem in a predictive dynamic continuum transportation system , Computer-Aided Civil and Infrastructure Engineering, v38 (2023), pp.2576-2596.
474. Z. Xu and C.-W. Shu, On the conservation property of positivity-preserving discontinuous Galerkin methods for stationary hyperbolic equations , Journal of Computational Physics, v490 (2023), 112304.
475. X. Gu, J. Cheng and C.-W. Shu, A high order positivity-preserving discontinuous Galerkin remapping method based on a moving mesh solver for ALE simulation of the compressible fluid flow , Communications in Computational Physics, v34 (2023), pp.1177-1214.
476. R.B. de R. Borges, F.C. Colman, N.D.P. da Silva, G.W.O. Dicati, J.E. Gubaua and C.-W. Shu, Approximated decompositions for computational continuum mechanics , Journal of Computational Physics, v495 (2023), 112576.
477. L.K. Araki, R.B. de R. Borges, N. Dicati P. da Silva and C.-W. Shu, Verification and validation of high-resolution inviscid and viscous conical nozzle flows , Communications on Applied Mathematics and Computation, v6 (2024), pp.533-549.
478. J. Zhu, C.-W. Shu and J. Qiu, RKDG methods with multi-resolution WENO limiters for solving steady-state problems on triangular meshes , Communications on Applied Mathematics and Computation, v6 (2024), pp.1575-1599.
479. D. Balsara, D. Bhoriya, C.-W. Shu and H. Kumar, Efficient finite difference WENO scheme for hyperbolic systems with non-conservative products , Communications on Applied Mathematics and Computation, v6 (2024), pp.907-962.
480. J. Cheng, N. Lei and C.-W. Shu, High order conservative Lagrangian scheme for three-temperature radiation hydrodynamics , Journal of Computational Physics, v496 (2024), 112595.
481. J. Zhu, C.-W. Shu and J. Qiu, Development and prospect of high-order WENO schemes , Scientia Sinica Mathematica (in Chinese), v54 (2024), pp.1-18.
482. M. Tan, J. Cheng and C.-W. Shu, The high order local discontinuous Galerkin schemes with variable-coefficient explicit-implicit-null time-marching for diffusion and dispersion equations , Communications on Applied Mathematics and Computation, to appear.
483. D. Balsara, D. Bhoriya, C.-W. Shu and H. Kumar, Efficient alternative finite difference WENO schemes for hyperbolic conservation laws , Communications on Applied Mathematics and Computation, to appear.
484. Y. Liu, J. Lu and C.-W. Shu, An entropy stable essentially oscillation-free discontinuous Galerkin method for hyperbolic conservation laws , SIAM Journal on Scientific Computing, v46 (2024), pp.A1132-A1159.
485. Z. Xu and C.-W. Shu, Local characteristic decomposition free high order finite difference WENO schemes for hyperbolic systems endowed with a coordinate system of Riemann invariants , SIAM Journal on Scientific Computing, v46 (2024), pp.A1352-A1372.
486. D. Balsara, D. Bhoriya, C.-W. Shu and H. Kumar, Efficient alternative finite difference WENO schemes for hyperbolic systems with non-conservative products , Communications on Applied Mathematics and Computation, to appear.
487. N. Lei, J. Cheng and C.-W. Shu, High order conservative Lagrangian schemes for two-dimensional radiation hydrodynamics equations in the equilibrium-diffusion limit , Journal of Computational Physics, v503 (2024), 112840.
488. F. Fu, C.-W. Shu, Q. Tao and B. Wu, Analysis of the boundary conditions for the ultraweak-local discontinuous Galerkin method of time-dependent linear fourth-order problems , Mathematics of Computation, v94 (2025), pp.123-158.
489. L. Yang, S. Li, Y. Jiang, C.-W. Shu and M. Zhang, Inverse Lax-Wendroff boundary treatment of discontinuous Galerkin method for 1D conservation laws , Communications on Applied Mathematics and Computation, to appear.
490. H. Liang, L. Yang, J. Du, C.-W. Shu and S.C. Wong, Modeling crowd pressure and turbulence through a mixed-type continuum approach , Transportmetrica B: Transport Dynamics, v12 (2024), 2328774.
491. A. Li, J. Li, J. Cheng and C.-W. Shu, High order compact Hermite reconstructions and their application in the improved two-stage fourth order time-stepping framework for hyperbolic problems: two-dimensional case , Communications in Computational Physics, v36 (2024), pp.1-29.
492. J. Li, C.-W. Shu and J. Qiu, Derivative-based finite-volume MR-HWENO scheme for steady-state problems , Communications in Computational Physics, to appear.
493. P. Mulet, J. Ruiz-Alvarez, C.-W. Shu and D.F. Yanez, A non-separable progressive multivariate WENO-2r point value , Applied Numerical Mathematics, v204 (2024), pp.26-47.
494. J. Lu, Y. Jiang, C.-W. Shu and M. Zhang, Analysis of a class of spectral volume methods for linear scalar hyperbolic conservation laws , Numerical Methods for Partial Differential Equations, v40 (2024), e23126.
495. B. Ye, J. Hu, C.-W. Shu and X. Zhong, Energy-conserving discontinuous Galerkin methods for the Vlasov-Ampere system with Dougherty-Fokker-Planck collision operator , Journal of Computational Physics, v514 (2024), 113219.
496. S. Liu, T. Li, Z. Cheng, Y. Jiang, C.-W. Shu and M. Zhang, A new type of simplified inverse Lax-Wendroff boundary treatment I: hyperbolic conservation laws , Journal of Computational Physics, v514 (2024), 113259.
497. H. Wang, Q. Tao, C.-W. Shu and Q. Zhang, Analysis of local discontinuous Galerkin methods with implicit-explicit time marching for linearized KdV equations , SIAM Journal on Numerical Analysis, v62 (2024), pp.2222-2248.
498. Y. Xu, C.-W. Shu and Q. Zhang, Stability analysis and error estimate of the explicit single step time marching discontinuous Galerkin method with stage-dependent numerical flux parameters for a linear hyperbolic equation in one dimension , Journal of Scientific Computing, v100 (2024), 64.
499. L. Yang, J. Du, S.C. Wong and C.-W. Shu, Boundedly rational departure time choice in a dynamic continuum user equilibrium model for an urban city , Transportation Research Part B, v187 (2024), 103038.
500. J. Cheng and C.-W. Shu, High order conservative finite difference WENO scheme for three-temperature radiation hydrodynamics , Journal of Computational Physics, v517 (2024), 113304.
501. Q. Tao, X. Chang, Y. Liu and C.-W. Shu, A local discontinuous Galerkin method for the Novikov equation , Mathematics of Computation, to appear.
502. Z. Xu and C.-W. Shu, A high-order well-balanced discontinuous Galerkin method for hyperbolic balance laws based on the Gauss-Lobatto quadrature rules , Journal of Scientific Computing, v101 (2024), 39.

Publications in Refereed Book Chapters, Proceedings and Lecture Notes

1. B. Cockburn and C.-W. Shu, A new class of non-oscillatory discontinuous Galerkin finite element methods for conservation laws, Proceedings of the 7th International Conference of Finite Element Methods in Flow Problems, UAH Press, 1989, pp.977-986.
2. S. Osher and C.-W. Shu, Recent progress on non-oscillatory shock capturing schemes, in Recent Advances in Computational Fluid Dynamics, C. C. Chao, S. A. Orszag and W. Shyy, Editors, Lecture Notes in Engineering, v43 (1989), Springer-Verlag. pp.316-333.
3. S. Osher and C.-W. Shu, Recent developments in non-oscillatory shock capturing methods, in The Numerical Modelling of Nonlinear Stellar Pulsations, J.R. Buchler, editor, Kluwer Academic Publishers, 1989. pp.263- 267.
4. C. Quillen and C.-W. Shu, Parallel implementation and application of high order ENO schemes, in Modeling and Simulation Volume 23, Part 5, Proceedings of the 23rd Annual Pittsburgh Conference on Modeling and Simulation, W. Vogt and M. Mickle, editors, University of Pittsburgh, 1992. pp.2739-2746.
5. J. Jerome and C.-W. Shu, Essentially Non-Oscillatory methods for two-dimensional hydrodynamic models, in Proceedings of the International Workshop on Computational Electronics, Beckman Institute, University of Illinois, May 1992, pp.83-86.
6. C. Gardner, J. Jerome and C.-W. Shu, The ENO method for the hydrodynamic model for semiconductor devices, in High Performance Computing, 1993: Grand Challenges in Computer Simulation, Adrian Tentner, editor, the Society for Computer Simulation, San Diego, 1993. pp.96-101.
7. G.-S. Jiang and C.-W. Shu, Stability of discontinuous Galerkin methods for general triangulations, In Developments in Theoretical and Applied Mechanics, Volume XVII, edited by I.C. Jong and F.A. Akl, Louisiana Tech University and University of Arkanas, 1994, pp.227-234.
8. J. Jerome and C.-W. Shu, Energy models for one-carrier transport in semiconductor devices, in IMA Volumes in Mathematics and Its Applications, v59, W. Coughran, J. Cole, P. Lloyd and J. White, editors, Springer-Verlag, 1994, pp.185-207.
9. J. Jerome and C.-W. Shu, Transport effect, hyperbolicity, and shock capturing algorithms for device simulations, in Proceedings of the Third International Workshop on Computational Electronics, Portland, Oregon, May 18-20, 1994, pp.252-255.
10. D. Gottlieb and C.-W. Shu, The resolution of the Gibbs phenomenon, ICASE Research Quarterly, Vol. 3, No. 2, June 1994, pp.5-7.
11. C.-W. Shu, Essentially non-oscillatory finite difference, finite volume and discontinuous Galerkin finite element methods for conservation laws, in Proceedings of the Third International Colloquium on Numerical Analysis, Plovdiv, Bulgaria, August 1994. D. Bainov and V. Covachev, editors, VSP International Science Publishers, the Netherlands, 1995, pp.171-180.
12. C.-W. Shu, On finite difference and finite element shock capturing methods for conservation laws, in Numerical Methods in Applied Sciences, W. Cai, Z.-C. Shi, C.-W. Shu and J. Xu, editors, Science Press, New York and Beijing, 1996, pp.169-187.
13. J. Jerome and C.-W. Shu, Energy transport systems for semiconductors: Analysis and simulation, in World Congress of Nonlinear Analysts '92, V. Lakshmikantham, Editor, Walter de Gruyter, Berlin and New York, 1996, pp. 3835-3846.
14. C.-W. Shu and P. Wong, A numerical study on the accuracy of Fourier spectral methods applied to the nonlinear Burgers equation, in Proceedings of the Third International Conference on Spectral and High Order Methods, A.V. Ilin and L.R. Scott, Editors, Houston Journal of Mathematics, 1996, pp. 131-138.
15. C. Hu and C.-W. Shu, High order weighted ENO schemes for unstructured meshes: preliminary results, Computational Fluid Dynamics 98, Invited Lectures, Minisymposia and Special Technological Sessions of the Fourth European Computational Fluid Dynamics Conference, K. Papailiou, D. Tsahalis, J. Periaux and D. Knorzer, Editors, John Wiley and Sons, v2, September 1998, pp.356-362.
16. C. Cercignani, I. Gamba, J. Jerome and C.-W. Shu, A domain decomposition method: a simulation study, in Proceedings of 1998 Sixth International Workshop on Computational Electronics (IWCE-6), Osaka University, Japan, October 19-21, 1998, IEEE Catalog Number 98EX116.
17. C.-W. Shu, Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws, in Advanced Numerical Approximation of Nonlinear Hyperbolic Equations, B. Cockburn, C. Johnson, C.-W. Shu and E. Tadmor (Editor: A. Quarteroni), Lecture Notes in Mathematics, volume 1697, Springer, 1998, pp.325-432.
18. G.-Q. Chen, J. Jerome, C.-W. Shu and D. Wang, Two carrier semiconductor device models with geometric structure, Modeling and Computation for Applications in Mathematics, Science, and Engineering, J. Jerome, editor, Oxford University Press, 1998, pp.103-140.
19. C.-W. Shu, High order ENO and WENO schemes for computational fluid dynamics, in High-Order Methods for Computational Physics, T.J. Barth and H. Deconinck, editors, Lecture Notes in Computational Science and Engineering, volume 9, Springer, 1999, pp.439-582.
20. B. Cockburn, G. Karniadakis and C.-W. Shu, The development of discontinuous Galerkin methods , in Discontinuous Galerkin Methods: Theory, Computation and Applications, B. Cockburn, G. Karniadakis and C.-W. Shu, editors, Lecture Notes in Computational Science and Engineering, volume 11, Springer, 2000, Part I: Overview, pp.3-50.
21. B. Cockburn, J. Jerome and C.-W. Shu, The utility of modeling and simulation in determining transport performance properties of semiconductors , in Discontinuous Galerkin Methods: Theory, Computation and Applications, B. Cockburn, G. Karniadakis and C.-W. Shu, editors, Lecture Notes in Computational Science and Engineering, volume 11, Springer, 2000, Part II: Invited Papers, pp.147-156.
22. B. Cockburn, M. Luskin, C.-W. Shu and E. Suli, Post-processing of Galerkin methods for hyperbolic problems , in Discontinuous Galerkin Methods: Theory, Computation and Applications, B. Cockburn, G. Karniadakis and C.-W. Shu, editors, Lecture Notes in Computational Science and Engineering, volume 11, Springer, 2000, Part III: Contributed Papers, pp.291-300.
23. C. Hu, O. Lepsky and C.-W. Shu, The effect of least square procedure for discontinuous Galerkin methods for Hamilton-Jacobi equations , in Discontinuous Galerkin Methods: Theory, Computation and Applications, B. Cockburn, G. Karniadakis and C.-W. Shu, editors, Lecture Notes in Computational Science and Engineering, volume 11, Springer, 2000, Part III: Contributed Papers, pp.343-348.
24. J.-G. Liu and C.-W. Shu, A numerical example on the performance of high order discontinuous Galerkin method for 2D incompressible flows , in Discontinuous Galerkin Methods: Theory, Computation and Applications, B. Cockburn, G. Karniadakis and C.-W. Shu, editors, Lecture Notes in Computational Science and Engineering, volume 11, Springer, 2000, Part III: Contributed Papers, pp.369-374.
25. C.-W. Shu, Different formulations of the discontinuous Galerkin method for the viscous terms , in Advances in Scientific Computing, Z.-C. Shi, M. Mu, W. Xue and J. Zou, editors, Science Press, 2001, pp.144-155.
26. C.-W. Shu, A survey of strong stability preserving high order time discretizations , in Collected Lectures on the Preservation of Stability under Discretization, D. Estep and S. Tavener, editors, SIAM, 2002, pp.51-65.
27. J.A. Carrillo, I. Gamba, O. Muscato and C.-W. Shu, Comparison of Monte Carlo and deterministic simulations of a silicon diode , in Transport in Transition Regimes, N.B. Ben Abdallah, A. Arnold, P. Degond, I. Gamba, R. Glassey, C. Levermore and C. Ringhofer, editors, IMA Volumes in Mathematics and Its Applications, v135, Springer-Verlag, New York, 2003, pp.75-84.
28. C.-W. Shu, An overview on high order numerical methods for convection dominated PDEs , in Hyperbolic Problems: Theory, Numerics, Applications, T.Y. Hou and E. Tadmor, editors, Springer-Verlag, Berlin, 2003, pp.79-88.
29. Y.-T. Zhang and C.-W. Shu, Third and fourth order weighted ENO schemes for Hamilton-Jacobi equations on 2D unstructured meshes , in Hyperbolic Problems: Theory, Numerics, Applications, T.Y. Hou and E. Tadmor, editors, Springer-Verlag, Berlin, 2003, pp.941-950.
30. L.-L. Feng, C.-W. Shu and M. Zhang, A hybrid cosmological hydrodynamic/N-body code based on the weighted essentially non-oscillatory scheme , Proceedings of the Fifth Sino-Germany Workshop on Cosmology and Galaxy Formation: The Formation, Evolution and Distribution of Galaxies, Y.P. Jing and G. Borner, editors, Prog. in Astro. (Suppl) vol 21, (2003) p18-23.
31. Y.-T. Zhang, J. Shi, C.-W. Shu and Y. Zhou, Resolution of high order WENO schemes and Navier-Stokes simulation of the Rayleigh-Taylor instability problem , in Computational Fluid and Solid Mechanics 2003, K.J. Bathe, Editor, the Proceedings of the Second MIT Conference on Computational Fluid and Solid Mechanics, June 17-20, 2003, volume 1, pp.1216-1218, Elsevier Science.
32. B. Cockburn, F. Li and C.-W. Shu, Discontinuous Galerkin methods for equations with divergence-free solutions: preliminary results , in Computational Fluid and Solid Mechanics 2003, K.J. Bathe, Editor, the Proceedings of the Second MIT Conference on Computational Fluid and Solid Mechanics, June 17-20, 2003, volume 2, pp.1900-1902, Elsevier Science.
33. S. Chen, W. E and C.-W. Shu, The heterogeneous multi-scale method based on the discontinuous Galerkin and the finite volume methods for hyperbolic problems , in Computational Fluid and Solid Mechanics 2005, Proceedings of the Third MIT Conference on Computational Fluid and Solid Mechanics, K.J. Bathe, Editor, Elsevier, 2005, pp.1072-1075.
34. M.J. Caceres, J.A. Carrillo, I.M. Gamba, A. Majorana and C.-W. Shu, Deterministic kinetic solvers for charged particle transport in semiconductor devices , in Transport Phenomena and Kinetic Theory --- Applications to Gases, Semiconductors, Photons, and Biological Systems, C. Cercignani and E. Gabetta, Editors, Birkhauser, 2007, pp.151-171.
35. J. Cheng and C.-W. Shu, High order ENO conservative remapping method on staggered grids for ALE methods: a review and an alternative momentum remapping , in Recent Progress in Scientific Computing, W. Liu, M. Ng and Z.-C. Shi, Editors, Science Press, Beijing, 2007, pp.40-56.
36. C.-W. Shu, High order numerical methods for time dependent Hamilton-Jacobi equations , in Mathematics and Computation in Imaging Science and Information Processing, S.S. Goh, A. Ron and Z. Shen, Editors, Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore, volume 11, World Scientific Press, Singapore, 2007, pp.47-91.
37. Y. Xia, L. Huang, S.C. Wong, M. Zhang, C.-W. Shu and W.H.K. Lam, The follow-the-crowd effect in a pedestrian flow model , the Proceedings of the 12th International Conference of Hong Kong Society for Transportation Studies, Hong Kong, December 2007, pp.309-317.
38. C.-W. Shu, Discontinuous Galerkin methods for convection dominated partial differential equations , the Proceedings of the Third International Congress of Chinese Mathematicians, Hong Kong, December 2004. AMS/IP Studies in Advanced Mathematics, Volume 42, International Press / American Mathematical Society, 2008, pp.63-73.
39. C.-W. Shu, Discontinuous Galerkin methods: general approach and stability , Numerical Solutions of Partial Differential Equations, S. Bertoluzza, S. Falletta, G. Russo and C.-W. Shu, Advanced Courses in Mathematics CRM Barcelona, Birkhauser, Basel, 2009, pp.149-201.
40. C.-W. Shu, High order accurate numerical methods for convection dominated PDEs , Y. Li, C.-W. Shu, R. Ye and K. Zuo, Editors, University of Science and Technology of China Press, Hefei, China, 2009, pp.139-153.
41. S. Noelle, Y. Xing and C.-W. Shu, High-order well-balanced schemes , Numerical Methods for Balance Laws, G. Puppo and G. Russo, editors, Quaderni di Matematica, volume 24, Seconda Universita di Napoli, 2009, pp.1-66.
42. C.-W. Shu, Discontinuous Galerkin methods , Encyclopedia of Aerospace Engineering, R. Blockley and W. Shyy, Editors, John Wiley & Sons Ltd, Chichester, United Kingdom, 2010, pp.661-668.
43. J.W. Jerome, M.A. Ratner, J.D. Servaites, C.-W. Shu and S. Tan, Simulation of the Buxton-Clarke model for organic photovoltaic cells , in Proceedings of the 14th International Workshop on Computational Electronics, IWCE, 26-29 October, 2010, Pisa, Italy. Pisa University Press, pp.195-198.
44. Y. Cheng, I.M. Gamba, A. Majorana and C.-W. Shu, Discontinuous Galerkin methods for the Boltzmann-Poisson systems in semiconductor device simulations , AIP Conference Proceedings, volume 1333, 2011, pp.890-895.
45. C.-W. Shu, A brief survey on high order accurate maximum principle satisfying and positivity preserving discontinuous Galerkin and finite volume schemes for conservation laws , Proceedings of the Fifth International Congress of Chinese Mathematicians (Beijing, December 2010). AMS/IP Studies in Advanced Mathematics, volume 51, 2012, pp.747-758.
46. S. Tan and C.-W. Shu, Inverse Lax-Wendroff procedure for numerical boundary conditions of hyperbolic equations: survey and new developments , in ``Advances in Applied Mathematics, Modeling and Computational Science'', R. Melnik and I. Kotsireas, Editors, Fields Institute Communications 66, Springer, New York, 2013, pp.41-63.
47. C.-W. Shu, Survey on discontinuous Galerkin methods for Hamilton-Jacobi equations , Proceedings of the Eighth International Conference on Scientific Computing and Applications, Contemporary Mathematics, American Mathematical Society, volume 586, 2013, pp.323-330.
48. J. Cheng and C.-W. Shu, Recent developments on the Lagrangian and remapping methods for compressible fluid flows , Numerical Methods for Hyperbolic Equations: Theory and Applications (conference proceedings in honor of Professor Toro on his 65th birthday), E. Vazquez-Cendon, A. Hidalgo, P. Garcia-Navarro and L. Cea, editors, CRC Press, Taylor and Francis Group, London, 2013, pp.9-19.
49. C.-W. Shu, Discontinuous Galerkin method for time dependent problems: Survey and recent developments , Recent Developments in Discontinuous Galerkin Finite Element Methods for Partial Differential Equations (2012 John H. Barrett Memorial Lectures), X. Feng, O. Karakashian and Y. Xing, editors, The IMA Volumes in Mathematics and Its Applications, volume 157, Springer, Switzerland, 2014, pp.25-62.
50. C.-W. Shu, Discontinuous Galerkin methods: Time dependent problems , Encyclopedia of Applied and Computational Mathematics, Bjorn Engquist, Editor, Springer-Verlag, Berlin-Heidelberg, 2015, pp.365-367.
51. C.-W. Shu, Error estimates for linear hyperbolic equations , Encyclopedia of Applied and Computational Mathematics, Bj\"{o}rn Engquist, Editor, Springer-Verlag, Berlin-Heidelberg, 2015, pp.440-445.
52. S. Zhang, X. Liu, H. Zhang and C.-W. Shu, High order and high resolution numerical schemes for computational aeroacoustics and their applications , in Fluid-Structure-Sound Interactions and Control, Y. Zhou et al, Editors, Lecture Notes in Mechanical Engineering, Springer, Berlin-Heidelberg, 2016, pp.27-32.
53. C.-W. Shu, Riemann problem and shock capturing schemes , in The Legacy of Bernhard Riemann after One Hundred and Fifty Years, L. Ji, F. Oort and S.-T. Yau, Editors, Advanced Lectures in Mathematics 35, Higher Education Press and International Press, Beijing-Boston, 2016, pp.681-689.
54. C.-W. Shu, Discontinuous Galerkin methods for time-dependent convection dominated problems: basics, recent developments and comparison with other methods , in Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations, Lecture Notes in Computational Science and Engineering, volume 114, G.R. Barrenechea, F. Brezzi, A. Cangiani and E.H. Georgoulis, editors, Springer, Switzerland, 2016, pp.369-397.
55. Y.-T. Zhang and C.-W. Shu, ENO and WENO schemes , in Handbook of Numerical Analysis, Volume 17, Handbook of Numerical Methods for Hyperbolic Problems: Basic and Fundamental Issues, R. Abgrall and C.-W. Shu, Editors, North-Holland, Elsevier, Amsterdam, 2016, pp.103-122.
56. S. Zhang, X. Liu, H. Zhang and C.-W. Shu, High order and high resolution numerical schemes for computational aeroacoustics and their applications , in Fluid-Structure-Sound Interactions and Control, Y. Zhou, A. Lucey, Y. Liu and L. Huang, Editors, Lecture Notes in Mechanical Engineering, Springer-Verlag, Berlin, 2016, pp.27-32.
57. C.-W. Shu and S. Tan, Inverse Lax-Wendroff procedure for numerical boundary treatment of hyperbolic equations , in Handbook of Numerical Analysis, Volume 18, Handbook of Numerical Methods for Hyperbolic Problems: Applied and Modern Issues, R. Abgrall and C.-W. Shu, Editors, North-Holland, Elsevier, Amsterdam, 2017, pp.23-52.
58. C.-W. Shu, Bound-preserving high order finite volume schemes for conservation laws and convection-diffusion equations , in Finite Volumes for Complex Applications VIII --- Methods and Theoretical Aspects, Proceedings of the Eighth Conference on Finite Volumes for Complex Applications (FVCA8), C. Cances and P. Omnes, Editors, Springer Proceedings in Mathematics and Statistics, volume 199, Springer, Switzerland, 2017, pp.3-14.
59. C.-W. Shu, IMEX time marching for discontinuous Galerkin methods , in International Conference of Numerical Analysis and Applied Mathematics (ICNAAM 2016), AIP Conf. Proc. 1863, AIP Publishing, 2017. 020006-1 -- 020006-3, doi: 10.1063/1.4992152
60. C.-W. Shu, Runge-Kutta and Lax-Wendroff discontinuous Galerkin methods for linear conservation laws , in International Conference of Numerical Analysis and Applied Mathematics (ICNAAM 2016), AIP Conf. Proc. 1863, AIP Publishing, 2017. 320010-1 -- 320010-3, doi: 10.1063/1.4992491
61. C.-W. Shu, A brief survey on high order numerical methods for convection dominated problems , Proceedings of the 6th International Congress of Chinese Mathematicians, Higher Education Press and International Press, ALM 36, 2017, pp.119-133.
62. C.-W. Shu, Bound-preserving high order schemes for hyperbolic equations: survey and recent developments , in Theory, Numerics and Applications of Hyperbolic Problems II, C. Klingenberg and M. Westdickenberg, Editors, Springer Proceedings in Mathematics & Statistics, Volume 237, Springer, 2018, pp.591-603.
63. V. Kucera and C.-W. Shu, Exponential scaling and the time growth of the error of DG for advection-reaction problems , in Numerical Mathematics and Advanced Applications, ENUMATH 2017, F.A. Radu et al., editors, Lecture Notes in Computational Science and Engineering 126, Springer, 2019, pp.963-971.
64. C.-W. Shu, A class of bound-preserving high order schemes: the main ideas and recent developments , Proceedings of the ICERM Symposium Celebrating 75 Years of Mathematics of Computation, AMS Contemporary Mathematics (CONM), v754, 2020, pp.247-259.
65. C.-W. Shu, Celebrating AWM's fiftieth anniversary: Mentoring PhD students , in Fifty Years of Women in Mathematics, J.L. Beery, S.J. Greenwald and C. Kessel, editors, Association for Women in Mathematics Series 28, Springer, 2022, pp.565-568.

Preprints

1. Z. Liu, Y. Jiang, C.-W. Shu and M. Zhang, High order inverse Lax-Wendroff procedure for fluid-structure interaction problems , submitted to Journal of Computational Physics.
2. Z. Liu, H. Liang, S.C. Wong, C.-W. Shu and M. Zhang, Capturing stochastic variabilities in pedestrian flows: a dynamic continuum modeling approach , submitted to Transportation Research Part B.
3. Z. Xu and C.-W. Shu, A well-balanced conservative high-order alternative finite difference WENO (A-WENO) method for hyperbolic balance laws , submitted to Advances in Water Resources.
4. W. Cao, C.-W. Shu and Z. Zhang, Unified analysis of the semidiscrete discontinuous Galerkin methods for 2-D hyperbolic equations on Cartesian meshes using ${\mathbb P}^k$ elements: optimal error estimates and superconvergence , submitted to Mathematics of Computation.
5. L. Vacek, C.-W. Shu and V. Kucera, L^2 stability and maximum principle for the discontinuous Galerkin method with Godunov-like numerical fluxes for traffic flows on networks , preprint.
6. C. Chen and C.-W. Shu, A second-order bound-preserving exponential scheme for degenerate parabolic equations , submitted to SIAM Journal on Scientific Computing.
7. Z. Liu, S.C. Wong, C.-W. Shu and M. Zhang, Multi-element probabilistic collocation solution for dynamic continuum pedestrian models with random inputs , submitted to Transportation Research Part C.
8. D. Bhoriya, D.S. Balsara, P. Chandrashekar and C.-W. Shu, Physical constraint preserving method for alternative finite difference WENO with non-conservative products , submitted to Journal of Scientific Computing.
9. A. Ditkowski, A. Le Blanc and C.-W. Shu, Error inhibiting methods for finite elements , submitted to ESAIM: Mathematical Modelling and Numerical Analysis ($M^{2}AN$).
10. K. Yu, J. Cheng, Y. Liu and C.-W. Shu, High-order implicit maximum-principle-preserving local discontinuous Galerkin methods for convection-diffusion equations , submitted to Mathematics of Computation.
11. Y. Chen, C.-W. Shu and S.-T. Yau, On the convergence of the discontinuous Galerkin scheme for Einstein-scalar equations , submitted to Mathematics of Computation.
12. W. Feng, J. Cheng and C.-W. Shu, Second order conservative Lagrangian DG schemes for compressible flow and their application in preserving spherical symmetry in two-dimensional cylindrical geometry , submitted to Journal of Computational Physics.
13. H. Wang, Q. Zhang, C.-W. Shu and Q. Tao, Stability and error analysis of a third order fully discrete local discontinuous Galerkin method for high order wave equations , submitted to Science China Mathematics.
14. M. Tan, J. Cheng and C.-W. Shu, High order finite difference scheme with explicit-implicit-null time-marching for the compressible Navier-Stokes equations , submitted to Journal of Computational Physics.
15. D.S. Balsara, D. Bhoriya and C.-W. Shu, An alternative finite difference WENO-like scheme with physical constraint preservation for divergence-preserving hyperbolic systems , submitted to Communications on Applied Mathematics and Computation.
16. Y. Xu, X. Meng, C.-W. Shu and Q. Zhang, Optimal error estimate of a discontinuous Galerkin method for one-dimensional linear hyperbolic equation with degenerate points moving along space-time curves , submitted to SIAM Journal on Numerical Analysis.

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