List of Publications

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.

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 non-oscillatory 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, ESAIM: Mathematical Modelling and Numerical Analysis (M^2 AN), v25 (1991), pp.337-361.
  12. S. Osher and C.-W. Shu, High order essentially non-oscillatory 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. Kan, U. Ravaioli, C.-W. Shu and 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 non-periodic 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.-S. Jiang and C.-W. Shu, On 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 A, v6 (1994), pp.49-58.
  24. J. Casper, C.-W. Shu and H.L. Atkins, Comparison of two formulations for high-order accurate essentially non-oscillatory 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. 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. 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 sub-interval from a Gegenbauer partial sum of a piecewise analytic function, Mathematics of Computation, v64 (1995), pp.1081-1095.
  29. C.-W. Shu and P. 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. Eisenberg, J. Jerome and C.-W. Shu,1 A 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 compressible 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, with 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. Kimia and C.-W. Shu, Geometric shock-capturing ENO schemes for subpixel interpolation, computation and curve evolution,, Computer Vision Graphics and Image Processing: 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. Atkins and C.-W. Shu, Quadrature-free implementation of the discontinuous Galerkin method for hyperbolic equations, AIAA Journal, v36 (1998), pp.775-782.
  44. G.-Q. Chen, J. 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. Gamba, J. 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. Gamba, J. 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. Gamba, J. 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. 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. Gamba, J. 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. Gamba and C.-W. Shu, Computational macroscopic approximations to the 1-D 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. Anile, J. Carrillo, I. 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. 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. Carrillo, I. 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 waves in 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. 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. 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, Multi domain WENO finite difference method with interpolation at sub-domain 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 discretization , 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. Carrillo, I. 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.295-307.
  86. Q. Zhang, M. Zhang, G. Jin, D.-Y. 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 non-oscillatory scheme , Astrophysical Journal, v612 (2004), pp.1-13.
  93. Y.-X. 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. 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 post-processing 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 multi-scale method based on the discontinuous Galerkin method for hyperbolic and parabolic problems , Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 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.-Z. 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 WENO 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, Multi-stage interaction of a shock wave and a strong vortex , Physics of Fluids, v17 (2005), article number 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. Carrillo, I. 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.100-134.
  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.-R. 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), article number 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), article number 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 a shock wave with an oblique vortex pair: shock dynamics and mechanism of sound generation , Physics of Fluids, v18 (2006), article number 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.-X. 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.-J. 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.-X. 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.-R. 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. S. Curtis, R.M. Kirby, J.K. Ryan and C.-W. Shu, Post-processing for the discontinuous Galerkin method over non-uniform meshes , SIAM Journal on Scientific Computing, v30 (2007), pp.272-289.
  152. Y.-J. Liu, C.-W. Shu, E. Tadmor and M. Zhang, Central discontinuous Galerkin methods on overlapping cells with a non-oscillatory hierarchical reconstruction , SIAM Journal on Numerical Analysis, v45 (2007), pp.2442-2467.
  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: A SIAM Interdisciplinary Journal, v7 (2008), pp.294-320.
  163. J. Zhu, J.-X. 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.-J. 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 limit , SIAM Journal on Scientific Computing, v31 (2008), pp.1249-1268.
  174. C.-W. Shu, High order weighted essentially non-oscillatory 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 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, A 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.-L. Xu, Y.-J. 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: the time scale of 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, to appear.
  189. Y.-Y. Liu, C.-W. Shu and M. Zhang, On the positivity of linear weights in WENO approximations , Acta Mathematicae Applicatae Sinica, 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.-L. Xu, Y.-J. Liu and C.-W. Shu, Hierarchical reconstruction for spectral volume method on unstructured grids , Journal of Computational Physics, v228 (2009), pp.6682-6702.
  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), article number 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, to appear.
  195. 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.
  196. Y. Xia, S.C. Wong and C.-W. Shu, Dynamic continuum pedestrian flow model with memory effect , Physical Review E, v79 (2009), article number 066113.
  197. Y. Xu and C.-W. Shu, Dissipative numerical methods for the Hunter-Saxton equation , Journal of Computational Mathematics, to appear.
  198. S. Zhang, H. Zhang and C.-W. Shu, Topological structure of shock induced vortex breakdown , Journal of Fluid Mechanics, v639 (2009), pp.343-372.
  199. C.-W. Shu, Efficient algorithms for solving partial differential equations with discontinuous solutions , Notices of the American Mathematical Society, to appear.
  200. 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 , Astrophysical Journal, v703 (2009), pp.1992-2003.
  201. J. Cheng and C.-W. Shu, High order schemes for CFD: A review , Chinese Journal of Computational Physics, v26 (2009), pp.633-655.
  202. B. Dong and C.-W. Shu, Analysis of a local discontinuous Galerkin method for fourth-order time-dependent problems , SIAM Journal on Numerical Analysis, v47 (2009), pp.3240-3268.
  203. 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.
  204. 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, to appear.
  205. Y.-J. Liu, C.-W. Shu and Z.-L. Xu, Hierarchical reconstruction with up to second degree remainder for solving nonlinear conservation laws , Nonlinearity, v22 (2009), pp.2799-2812.
  206. Y. Xia, Y. Xu and C.-W. Shu, Local discontinuous Galerkin methods for the generalized Zakharov system , Journal of Computational Physics, to appear.
  207. 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, to appear.

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. 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.
  38. 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.
  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.

Preprints

  1. S. Noelle, Y. Xing and C.-W. Shu, High-order well-balanced schemes , to appear in Numerical Methods for Relaxation Systems and Balance Equations, G. Puppo and G. Russo, editors, Quaderni di Matematica, Dipartimento di Matematica, Seconda Universita di Napoli, Italy.
  2. Y.-Q. Jiang, T. Xiong, S.C. Wong, P. Zhang, C.-W. Shu, M. Zhang and W.H.K. Lam, A dynamic continuum model for bi-directional pedestrian flows , submitted to Acta Mathematica Scientia.
  3. T. Xiong, M. Zhang, Y.-T. Zhang and C.-W. Shu, Fifth order fast sweeping WENO scheme for static Hamilton-Jacobi equations with accurate boundary treatment , submitted to Journal of Scientific Computing.
  4. X. Zhang and C.-W. Shu, A genuinely high order total variation diminishing scheme for one-dimensional scalar conservation laws , submitted to SIAM Journal on Numerical Analysis.
  5. 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 flow , submitted to Computer Aided Civil and Infrastructure Engineering.
  6. Y.-T. Zhang, S. Chen, F. Li, H. Zhao and C.-W. Shu, Uniformly accurate discontinuous Galerkin fast sweeping methods for Eikonal equations , submitted to SIAM Journal on Scientific Computing.
  7. Q. Zhang and C.-W. Shu, Stability analysis and a priori error estimates to the third order explicit Runge-Kutta discontinuous Galerkin Method for scalar conservation laws , submitted to SIAM Journal on Numerical Analysis.
  8. O. Bokanowski, Y. Cheng and C.-W. Shu, A discontinuous Galerkin solver for front propagation , submitted to SIAM Journal on Scientific Computing.
  9. X. Zhang and C.-W. Shu, On maximum-principle-satisfying high order schemes for scalar conservation laws , submitted to Journal of Computational Physics.
  10. 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 , submitted to Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal.

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