List of Publications
Books
Publications in Refereed Journals (Appeared or Accepted)
Publications in Proceedings, Lecture Notes, and Technical Reports
Preprints
 Numerical Methods in Applied Sciences,
W. Cai, Z.C. Shi, C.W. Shu and
J. Xu, editors, Science Press, New York and Beijing, 1996.

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.

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.

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.

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.

Selected New Numerical Methods for Computational Fluid Dynamics
(in Chinese)
,
R.X. Liu and C.W. Shu, Science Press,
Beijing, 2003.

Recent Advances in Computational Sciences
,
C.W. Shu and N. Yan, editors,
World Scientific, 2008.

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.

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.

Strong Stability Preserving RungeKutta and Multistep Time
Discretizations
,
S. Gottlieb, D. Ketcheson and C.W. Shu,
World Scientific, Singapore, 2011.
 C.W. Shu,
TVB uniformly highorder schemes for conservation laws,
Mathematics of Computation, v49 (1987), pp.105121.
 C.W. Shu,
TVB boundary treatment for numerical solutions of
conservation laws, Mathematics of Computation,
v49 (1987), pp.123134.
 C.W. Shu,
Totalvariationdiminishing time discretizations,
SIAM Journal on Scientific and Statistical Computing, v9
(1988), pp.10731084.
 C.W. Shu and S. Osher,
Efficient implementation of essentially
nonoscillatory shockcapturing schemes,
Journal of Computational Physics, v77 (1988), pp.439471.
 B. Cockburn and C.W. Shu,
TVB RungeKutta local projection discontinuous
Galerkin finite element method for conservation laws II:
general framework, Mathematics of
Computation, v52 (1989), pp.411435.
 C.W. Shu and S. Osher,
Efficient implementation of essentially non
oscillatory shockcapturing schemes II,
Journal of Computational Physics, v83 (1989), pp.3278.
 B. Cockburn, S.Y. Lin and C.W. Shu,
TVB RungeKutta local projection discontinuous
Galerkin finite element method for conservation laws III:
onedimensional systems,
Journal of Computational Physics, v84 (1989), pp.90113.
 W. Cai, D. Gottlieb and C.W. Shu,
Essentially nonoscillatory spectral Fourier methods
for shock wave calculations,
Mathematics of Computation, v52 (1989), pp.389410.
 B. Cockburn, S. Hou and C.W. Shu,
The RungeKutta local projection discontinuous
Galerkin finite element method for conservation laws IV:
the multidimensional case,
Mathematics of Computation, v54 (1990), pp.545581.
 C.W. Shu,
Numerical experiments on the accuracy of ENO and
modified ENO schemes, Journal of Scientific Computing,
v5 (1990), pp.127149.
 B. Cockburn and C.W. Shu,
The RungeKutta local projection P1discontinuousGalerkin
finite element method for scalar conservation laws,
Mathematical Modelling and Numerical
Analysis (M^2 AN), v25 (1991), pp.337361.
 S. Osher and C.W. Shu,
Highorder essentially nonoscillatory schemes for
HamiltonJacobi equations, SIAM Journal
on Numerical Analysis, v28 (1991), pp.907922.
 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.424429.
 C.W. Shu, T.A. Zang, G. Erlebacher, D. Whitaker and S. Osher,
Highorder ENO schemes applied to two and threedimensional
compressible flow,
Applied Numerical Mathematics,
v9 (1992), pp.4571.
 W. Cai, D. Gottlieb and C.W. Shu,
On onesided filters for spectral Fourier
approximations of discontinuous functions,
SIAM Journal on Numerical Analysis v29 (1992), pp.905916.
 D. Chen, E.C. Kan, U. Ravaioli, C.W. Shu and R.W. Dutton,
An improved energy transport model including
nonparabolicity and nonMaxwellian distribution effects,
IEEE Electron Device Letters, v13 (1992), pp.2628.
 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.8198.
 W. Cai and C.W. Shu,
Uniform highorder spectral methods for one and
twodimensional Euler equations,
Journal of Computational Physics, v104 (1993), pp.427443.
 W. E and C.W. Shu,
Effective equations and the inverse cascade theory for
Kolmogorov flows,
Physics of Fluids A, v5 (1993), pp.9981010.
 W. E and C.W. Shu,
A numerical resolution study of high order
essentially nonoscillatory schemes applied to incompressible
flow,
Journal of
Computational Physics, v110 (1994), pp.3946.
 B. Cockburn and C.W. Shu,
Nonlinearly stable compact schemes for shock
calculations,
SIAM Journal on Numerical Analysis, v31 (1994), pp.607627.
 G. Jiang and C.W. Shu,
On a cell entropy inequality for discontinuous Galerkin
methods,
Mathematics of Computation, v62 (1994), pp.531538.
 W. E and C.W. Shu,
Smallscale structures in
Boussinesq convection,
Physics of Fluids, v6 (1994), pp.4958.
 J. Casper, C.W. Shu and H. Atkins,
Comparison of two formulations for highorder
accurate essentially nonoscillatory schemes,
AIAA Journal, v32 (1994), pp.19701977.
 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.2737.
 Z. Chen, B. Cockburn, J.W. Jerome and C.W. Shu,
MixedRKDG finite element methods for the 2D hydrodynamic model
for semiconductor device simulation,
VLSI Design, v3 (1995), pp.145158.
 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.131143.
 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.10811095.
 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.357369.
 J. Jerome and C.W. Shu,
Transport effects and characteristic modes in the modeling and
simulation of submicron devices,
IEEE Transactions on ComputerAided Design of Integrated Circuits and
Systems, v14 (1995), pp.917923.
 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.511526.
 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.23042322.
 D. Gottlieb and C.W. Shu,
On the Gibbs phenomenon III: recovering exponential accuracy in
a subinterval from a spectral partial sum of a piecewise
analytic function,
SIAM Journal on Numerical Analysis, v33 (1996), pp.280290.
 B. Perthame and C.W. Shu,
On positive preserving finite volume schemes for
Euler equations,
Numerische Mathematik, v73 (1996), pp.119130.
 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.1526.
 G.S. Jiang and C.W. Shu,
Efficient implementation of weighted ENO schemes,
Journal of Computational Physics, v126 (1996), pp.202228.
 C.W. Shu and Y. Zeng,
High order essentially nonoscillatory scheme for viscoelasticity
with fading memory,
Quarterly of Applied Mathematics, v55 (1997), pp.459484.
 G. Erlebacher, M.Y. Hussaini and C.W. Shu,
Interaction of a shock with a longitudinal vortex,
Journal of Fluid Mechanics, v337 (1997), pp.129153.
 D. Gottlieb and C.W. Shu,
On the Gibbs phenomenon and its resolution,,
SIAM Review, v30 (1997), pp.644668.
 K. Siddiqi, B.B. Kimia and C.W. Shu,
Geometric shockcapturing ENO schemes for subpixel interpolation,
computation and curve evolution,,
Graphical
Models and Image Processing (CVGIP:GMIP), v59 (1997), pp.278301.
 S. Gottlieb and C.W. Shu,
Total variation diminishing RungeKutta schemes,
Mathematics of Computation, v67 (1998), pp.7385.
 B. Cockburn and C.W. Shu,
The RungeKutta discontinuous Galerkin method for conservation laws V:
multidimensional systems,
Journal of Computational Physics, v141 (1998), pp.199224.
 H.L. Atkins and C.W. Shu,
Quadraturefree implementation of discontinuous Galerkin method
for hyperbolic equations,
AIAA Journal, v36 (1998), pp.775782.
 G.Q. Chen, J.W. Jerome and C.W. Shu,
Analysis and simulation of extended hydrodynamic models:
the multivalley Gunn oscillator and MESFET symmetries,
VLSI Design, v6 (1998), pp.277282.
 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.135141.
 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.275282.
 B. Cockburn and C.W. Shu,
The local discontinuous Galerkin method for timedependent
convectiondiffusion systems,
SIAM Journal on Numerical Analysis, v35 (1998), pp.24402463.
 P. Montarnal and C.W. Shu,
Real gas computation using an energy relaxation method and highorder
WENO schemes,
Journal of Computational Physics, v148 (1999), pp.5980.
 C. Hu and C.W. Shu,
Weighted essentially nonoscillatory schemes on triangular meshes,
Journal of Computational Physics, v150 (1999), pp.97127.
 C. Hu and C.W. Shu,
A discontinuous Galerkin finite element method for HamiltonJacobi
equations,
SIAM Journal on Scientific Computing, v21 (1999), pp.666690.
 O. Lepsky, C. Hu and C.W. Shu,
The
Analysis of the discontinuous Galerkin method for HamiltonJacobi
equations,
Applied Numerical Mathematics, v33 (2000), pp.423434.
 C. Cercignani, I.M. Gamba, J.W. Jerome and C.W. Shu,
Device benchmark comparisons via kinetic, hydrodynamic, and highfield
models,
Computer Methods in Applied Mechanics and Engineering,
v181 (2000), pp.381392.
 D.S. Balsara and C.W. Shu,
Monotonicity preserving weighted essentially nonoscillatory schemes
with increasingly high order of accuracy
,
Journal of Computational Physics
,
v160 (2000), pp.405452.
 J.G. Liu and C.W. Shu,
A highorder discontinuous Galerkin method for 2D incompressible flows
,
Journal of Computational Physics
,
v160 (2000), pp.577596.
 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.525536.
 J.A. Carrillo, I.M. Gamba and C.W. Shu,
Computational macroscopic approximations to the onedimensional
relaxationtime kinetic system for semiconductors
,
Physica D
,
v146 (2000), pp.289306.
 S. Gottlieb, C.W. Shu and E. Tadmor,
Strong stabilitypreserving highorder time discretization methods
,
SIAM Review,
v43 (2001), pp.89112.
 T. Zhou, Y. Guo and C.W. Shu,
Numerical study on Landau damping
,
Physica D, v157 (2001), pp.322333.
 A. Arnold, J.A. Carrillo, I. Gamba and C.W. Shu,
Low and high field scaling limits for the Vlasov and
WignerPoissonFokkerPlanck systems
,
Transport Theory and Statistical Physics,
v30 (2001), pp.121153.
 T. Zhou, Y. Li and C.W. Shu,
Numerical comparison of WENO finite volume and RungeKutta
discontinuous Galerkin methods
,
Journal of Scientific Computing,
v16 (2001), pp.145171.
 B. Cockburn and C.W. Shu,
RungeKutta Discontinuous Galerkin methods for convectiondominated
problems
,
Journal of Scientific Computing,
v16 (2001), pp.173261.
 M.A. Anile, J.A. Carrillo, I.M. Gamba and C.W. Shu,
Approximation of the BTE by a relaxationtime operator:
simulations for a 50nmchannel Si diode
,
VLSI Design
,
v13 (2001), pp.349354.
 K. Banoo, J.H. Rhew, M. Lundstrom, C.W. Shu and J.W. Jerome,
Simulating quasiballistic transport in Si nanotransistors
,
VLSI Design
,
v13 (2001), pp.513.
 J. Shi, C. Hu and C.W. Shu,
A technique of treating negative weights in WENO schemes
,
Journal of Computational Physics, v175 (2002), pp.108127.
 J. Yan and C.W. Shu,
A local discontinuous Galerkin method for KdV type equations
,
SIAM Journal on Numerical Analysis, v40 (2002), pp.769791.
 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.2747.
 J.A. Carrillo, I.M. Gamba, A. Majorana and C.W. Shu,
A WENOsolver for the 1D nonstationary BoltzmannPoisson system
for semiconductor devices
,
Journal of Computational Electronics, v1 (2002), pp.365370.
 P. Lin and C.W. Shu,
Numerical solution of a virtual internal bond model for material
fracture
,
Physica D, v167 (2002), pp.101121.
 J. Qiu and C.W. Shu,
On the construction, comparison, and local characteristic
decomposition for highorder central WENO schemes
,
Journal of Computational Physics, v183 (2002), pp.187209.
 G.D. Jin, D.Y. Liu and C.W. Shu,
Propagation and decay of concentration wave in the liquidsolid
pulsed fluidized beds
,
The Chinese Journal of Process Engineering (in Chinese),
v2 (2002), pp.392399.
 C.W. Shu,
Highorder finite difference and finite volume WENO schemes
and discontinuous Galerkin methods for CFD
,
International Journal of Computational Fluid Dynamics,
v17 (2003), pp.107118.
 B. Cockburn, M. Luskin, C.W. Shu and E. Suli,
Enhanced accuracy by postprocessing for finite element methods for
hyperbolic equations
,
Mathematics of Computation, v72 (2003), pp.577606.
 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.111132.
 Y.T. Zhang and C.W. Shu,
High order WENO schemes for HamiltonJacobi equations on triangular meshes
,
SIAM Journal on Scientific Computing, v24 (2003), pp.10051030.
 J.A. Carrillo, I.M. Gamba, A. Majorana and C.W. Shu,
A WENOsolver for the transients of BoltzmannPoisson system for
semiconductor devices: performance and comparisons with Monte Carlo methods
,
Journal of Computational Physics, v184 (2003), pp.498525.
 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.309341.
 K. Sebastian and C.W. Shu,
Multidomain WENO finite difference method with
interpolation at subdomain interfaces
,
Journal of Scientific Computing, v19 (2003), pp.405438.
 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.395413.
 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.690696.
 J. Qiu and C.W. Shu,
Finite difference WENO schemes with LaxWendrofftype time discretizations
,
SIAM Journal on Scientific Computing, v24 (2003), pp.21852198.
 M. Zhang, C.W. Shu, G.C.K. Wong and S.C. Wong,
A weighted essentially nonoscillatory numerical scheme for a
multiclass LighthillWhithamRichards traffic flow model
,
Journal of Computational Physics, v191 (2003), pp.639659.
 Y.T. Zhang, J. Shi, C.W. Shu and Y. Zhou,
Numerical viscosity and resolution of highorder
weighted essentially nonoscillatory
schemes for compressible flows with high Reynolds numbers
,
Physical Review E, v68 (2003), 046709.
 J. Qiu and C.W. Shu,
Hermite WENO schemes and their application as limiters for
RungeKutta discontinuous Galerkin method: one dimensional case
,
Journal of Computational Physics, v193 (2003), pp.115135.
 J.A. Carrillo, I.M. Gamba, A. Majorana and C.W. Shu,
A direct solver for 2D nonstationary BoltzmannPoisson systems
for semiconductor devices: a MESFET simulation by WENOBoltzmann schemes
,
Journal of Computational Electronics, v2 (2003), pp.375380.
 J. Ryan and C.W. Shu,
On a onesided postprocessing technique for the discontinuous
Galerkin methods
,
Methods and Applications of Analysis, v10 (2003),
pp.295308.
 Q. Zhang, M. Zhang, G. Jin, D. Liu and C.W. Shu,
Modeling, numerical methods,
and simulation for particlefluid twophase flow problems
,
Computers and Mathematics with Applications, v47 (2004), pp.14371462.
 Y. Guo, C.W. Shu and T. Zhou,
The dynamics of a plane diode
,
SIAM Journal on Mathematical Analysis, v35 (2004), pp.16171635.
 B. Cockburn, F. Li and C.W. Shu,
Locally divergencefree
discontinuous Galerkin methods for the Maxwell equations
,
Journal of Computational Physics, v194 (2004), pp.588610.
 Q. Zhang and C.W. Shu,
Error estimates to smooth solutions of RungeKutta
discontinuous Galerkin methods for scalar conservation laws
,
SIAM Journal on Numerical Analysis, v42 (2004), pp.641666.
 D. Levy, C.W. Shu and J. Yan,
Local discontinuous Galerkin methods for nonlinear dispersive equations
,
Journal of Computational Physics, v196 (2004), pp.751772.
 Y. Xu and C.W. Shu,
Local discontinuous Galerkin methods for three classes of nonlinear wave equations
,
Journal of Computational Mathematics, v22 (2004), pp.250274.
 L.L. Feng, C.W. Shu and M. Zhang,
A hybrid cosmological hydrodynamic/Nbody code based on a weighted
essentially nonoscillatory scheme
,
Astrophysical Journal, v612 (2004), pp.113.
 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.263267.
 F. Li and C.W. Shu,
Locally divergencefree discontinuous Galerkin methods for MHD equations
,
Journal of Scientific Computing, v2223 (2005), pp.413442.
 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.581592.
 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.597612.
 C.W. Shu, W.S. Don, D. Gottlieb, O. Schilling and L. Jameson,
Numerical convergence study of nearly incompressible, inviscid TaylorGreen vortex flow
,
Journal of Scientific Computing, v24 (2005), pp.569595.
 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.821843.
 J. Qiu and C.W. Shu,
RungeKutta discontinuous Galerkin method using WENO limiters
,
SIAM Journal on Scientific Computing, v26 (2005), pp.907929.
 J. Qiu and C.W. Shu,
Hermite WENO schemes and their application as limiters for
RungeKutta discontinuous Galerkin method II: two dimensional case
,
Computers and Fluids, v34 (2005), pp.642663.
 J. Qiu and C.W. Shu,
Hermite WENO schemes for HamiltonJacobi equations
,
Journal of Computational Physics, v204 (2005), pp.8299.
 F. Li and C.W. Shu,
Reinterpretation and simplified implementation of
a discontinuous Galerkin method for HamiltonJacobi equations
,
Applied Mathematics Letters, v18 (2005), pp.12041209.
 Y. Xu and C.W. Shu,
Local discontinuous Galerkin methods for nonlinear Schrodinger equations
,
Journal of Computational Physics, v205 (2005), pp.7297.
 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.871894.
 Z. Xu and C.W. Shu,
Antidiffusive flux corrections for high order finite difference WENO schemes
,
Journal of Computational Physics, v205 (2005), pp.458485.
 J. Qiu, M. Dumbser and C.W. Shu,
The discontinuous Galerkin method with LaxWendroff type time
discretizations
,
Computer Methods in Applied Mechanics and Engineering,
v194 (2005), pp.45284543.
 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.206227.
 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.129132.
 F. Filbet and C.W. Shu,
Approximation of hyperbolic models for chemosensitive movement
,
SIAM Journal on Scientific Computing, v27 (2005), pp.850872.
 J. Qiu and C.W. Shu,
A comparison of troubledcell indicators for
RungeKutta discontinuous Galerkin methods using weighted
essentially nonoscillatory limiters
,
SIAM Journal on Scientific Computing, v27 (2005), pp.9951013.
 Y. Xu and C.W. Shu,
Local discontinuous Galerkin methods for two classes of twodimensional
nonlinear wave equations
,
Physica D, v208 (2005), pp.2158.
 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.
 F. Filbet, Y. Guo and C.W. Shu,
Analysis of the relativistic VlasovMaxwell model in an interval
,
Quarterly of Applied Mathematics, v63 (2005), pp.691714.
 Z. Xu and C.W. Shu,
Antidiffusive high order WENO schemes for HamiltonJacobi equations
,
Methods and Applications of Analysis, v12 (2005), pp.169190.
 Y. Xu and C.W. Shu,
Local discontinuous Galerkin methods for the KuramotoSivashinsky
equations and the Itotype coupled KdV equations
,
Computer Methods in Applied Mechanics and Engineering, v195 (2006),
pp.34303447.
 J. Qiu, B.C. Khoo and C.W. Shu,
A numerical study for the performance of the RungeKutta
discontinuous Galerkin method based on different numerical fluxes
,
Journal of Computational Physics, v212 (2006), pp.540565.
 P. Zhang, S.C. Wong and C.W. Shu,
A weighted essentially nonoscillatory numerical scheme for a multiclass
traffic flow model on an inhomogeneous highway
,
Journal of Computational Physics, v212 (2006), pp.739756.
 J.A. Carrillo, I.M. Gamba, A. Majorana and C.W. Shu,
2D semiconductor device simulations by WENOBoltzmann schemes:
efficiency, boundary conditions and comparison to Monte Carlo methods
,
Journal of Computational Physics, v214 (2006), pp.5580.
 Y. Xing and C.W. Shu,
Highorder wellbalanced finite difference WENO schemes for a class
of hyperbolic systems with source terms
,
Journal of Scientific Computing, v27 (2006), pp.477494.
 Y. Xing and C.W. Shu,
High order wellbalanced finite volume WENO schemes and discontinuous Galerkin
methods for a class of hyperbolic systems with source terms
,
Journal of Computational Physics, v214 (2006), pp.567598.
 Y. Xing and C.W. Shu,
A new approach of high order wellbalanced finite volume WENO
schemes and discontinuous Galerkin methods for a class of
hyperbolic systems with source terms
,
Communications in Computational Physics, v1 (2006), pp.101135.
 S. Gottlieb, D. Gottlieb and C.W. Shu,
Recovering highorder accuracy in WENO computations of steadystate hyperbolic systems
,
Journal of Scientific Computing, v28 (2006), pp.307318.
 C.S. Chou and C.W. Shu,
High order residual distribution conservative finite difference WENO
schemes for steady state problems on nonsmooth meshes
,
Journal of Computational Physics, v214 (2006), pp.698724.
 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.17201731.
 P. He, J. Liu, L.L. Feng, C.W. Shu and L.Z. Fang,
Lowredshift cosmic baryon fluid on large scales and SheLeveque universal scaling
,
Physical Review Letters, v96 (2006), 051302.
 L. Yuan and C.W. Shu,
Discontinuous Galerkin method based on nonpolynomial
approximation spaces
,
Journal of Computational Physics, v218 (2006), pp.295323.
 Z. Xu and C.W. Shu,
Antidiffusive finite difference WENO methods for shallow water
with transport of pollutant
,
Journal of Computational Mathematics, v24 (2006), pp.239251.
 Y.T. Zhang, C.W. Shu and Y. Zhou,
Effects of shock waves on RayleighTaylor instability
,
Physics of Plasmas, v13 (2006), 062705.
 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.110.
 Q. Zhang and C.W. Shu,
Error estimates to smooth solutions of RungeKutta discontinuous
Galerkin method for symmetrizable systems of conservation laws
,
SIAM Journal on Numerical Analysis, v44 (2006), pp.17031720.
 Y. Xing and C.W. Shu,
Application of high order wellbalanced schemes to a class of
hyperbolic systems with source terms
,
Boletin de la Sociedad Espanola de Matematica Aplicada,
v34 (2006), pp.6980.
 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.
 D. Levy, S. Nayak, C.W. Shu and Y.T. Zhang,
Central WENO schemes for HamiltonJacobi equations on triangular meshes
,
SIAM Journal on Scientific Computing, v28 (2006), pp.22292247.
 M.J. Caceres, J.A. Carrillo, I. Gamba, A. Majorana and C.W. Shu,
DSMC versus WENOBTE: a double gate MOSFET example
,
Journal of Computational Electronics, v5 (2006), pp.471474.
 F. Li and C.W. Shu,
A localstructurepreserving local discontinuous Galerkin
method for the Laplace equation
,
Methods and Applications of Analysis, v13 (2006), pp.215234.
 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.629645.
 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.273305.
 Y. Cheng and C.W. Shu,
A discontinuous Galerkin finite element method for
directly solving the HamiltonJacobi equations
,
Journal of Computational Physics, v223 (2007), pp.398415.
 J. Shen, C.W. Shu and M. Zhang,
High resolution schemes for a hierarchical sizestructured model
,
SIAM Journal on Numerical Analysis, v45 (2007), pp.352370.
 C.S. Chou and C.W. Shu,
High order residual distribution conservative finite difference WENO
schemes for convectiondiffusion steady state problems on nonsmooth meshes
,
Journal of Computational Physics, v224 (2007), pp.9921020.
 Y. Xu and C.W. Shu,
Error estimates of the semidiscrete local discontinuous Galerkin
method for nonlinear convectiondiffusion and KdV equations
,
Computer Methods in Applied Mechanics and Engineering,
v196 (2007), pp.38053822.
 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.398409.
 Y. Liu, C.W. Shu, E. Tadmor and M. Zhang,
Nonoscillatory hierarchical reconstruction for central
and finite volume schemes
,
Communications in Computational Physics, v2 (2007), pp.933963.
 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.677693.
 S. Chen, W. E, Y. Liu and C.W. Shu,
A discontinuous Galerkin implementation of a
domain decomposition method for kinetichydrodynamic coupling
multiscale problems in gas dynamics and device simulations
,
Journal of Computational Physics, v225 (2007), pp.13141330.
 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.19.
 S. Noelle, Y. Xing and C.W. Shu,
Highorder wellbalanced finite volume WENO schemes for
shallow water equation with moving water
,
Journal of Computational Physics, v226 (2007), pp.2958.
 Y. Xia, Y. Xu and C.W. Shu,
Local discontinuous Galerkin methods for the CahnHilliard type equations
,
Journal of Computational Physics, v227 (2007), pp.472491.
 J. Shen, C.W. Shu and M. Zhang,
A high order WENO scheme for a hierarchical sizestructured population model
,
Journal of Scientific Computing, v33 (2007), pp.279291.
 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.15671596.
 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 (2007), pp.272289.
 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.24422467.
 J. Cheng and C.W. Shu,
A high order accurate conservative remapping method on staggered meshes
,
Applied Numerical Mathematics, v58 (2008), pp.10421060.
 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.699730.
 Y. Xu and C.W. Shu,
A local discontinuous Galerkin method for the CamassaHolm equation
,
SIAM Journal on Numerical Analysis, v46 (2008), pp.19982021.
 J.M. Qiu and C.W. Shu,
Convergence of Godunovtype schemes for scalar conservation laws
under large time steps
,
SIAM Journal on Numerical Analysis, v46 (2008), pp.22112237.
 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.111.
 L. Yuan and C.W. Shu,
Discontinuous Galerkin method for a class of elliptic multiscale problems
,
International Journal for Numerical Methods in Fluids, v56 (2008), pp.10171032.
 W. Chen, S.C. Wong and C.W. Shu,
Efficient implementation of the shockfitting algorithm for the
LighthillWhithamRichards traffic flow model
,
International Journal for Numerical Methods in Engineering,
v74 (2008), pp.554600.
 Y. Lu, S.C. Wong, M. Zhang, C.W. Shu and W. Chen,
Explicit construction of entropy solutions for the LighthillWhithamRichards
traffic flow model with a piecewise quadratic flowdensity relationship
,
Transportation Research Part B, v42 (2008), pp.355372.
 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.633656.
 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.294320.
 J. Zhu, J. Qiu, C.W. Shu and M. Dumbser,
RungeKutta discontinuous Galerkin method using WENO limiters II: unstructured meshes
,
Journal of Computational Physics, v227 (2008), pp.43304353.
 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.593607.
 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.337350.
 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.10081024.
 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.336346.
 Y. Cheng, I.M. Gamba, A. Majorana and C.W. Shu,
Discontinuous Galerkin solver for BoltzmannPoisson transients
,
Journal of Computational Electronics, v7 (2008), pp.119123.
 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.72947321.
 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.81918208.
 J.M. Qiu and C.W. Shu,
Convergence of high order finite volume weighted essentially nonoscillatory
scheme and discontinuous Galerkin method for nonconvex conservation laws
,
SIAM Journal on Scientific Computing, v31 (2008), pp.584607.
 Y. Cheng and C.W. Shu,
Superconvergence and time evolution of discontinuous Galerkin finite element solutions
,
Journal of Computational Physics, v227 (2008), pp.96129627.
 Y. Xu and C.W. Shu,
Local discontinuous Galerkin method for the HunterSaxton
equation and its zeroviscosity and zerodispersion limits
,
SIAM Journal on Scientific Computing, v31 (2008), pp.12491268.
 C.W. Shu,
High order weighted essentially nonoscillatory schemes for
convection dominated problems
,
SIAM Review, v51 (2009), pp.82126.
 Y.T. Zhang and C.W. Shu,
Third order WENO scheme on three dimensional tetrahedral meshes
,
Communications in Computational Physics, v5 (2009), pp.836848.
 Y. Xia, Y. Xu and C.W. Shu,
Application of the local discontinuous Galerkin method for the
AllenCahn/CahnHilliard system
,
Communications in Computational Physics, v5 (2009), pp.821835.
 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.376390.
 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.127141.
 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.360374.
 S. Gottlieb, D.I. Ketcheson and C.W. Shu,
High order strong stability preserving time discretizations
,
Journal of Scientific Computing, v38 (2009), pp.251289.
 L. Huang, Y. Xia, S.C. Wong, C.W. Shu, M. Zhang and W.H.K. Lam,
Dynamic continuum model for bidirectional pedestrian flows
,
Proceedings of the Institution of Civil Engineers:
Engineering and Computational Mechanics, v162 (2009), pp.6775.
 Y. Cheng and C.W. Shu,
Superconvergence of local discontinuous Galerkin methods for onedimensional convectiondiffusion equations
,
Computers and Structures, v87 (2009), pp.630641.
 Z. Xu, Y. Liu and C.W. Shu,
Hierarchical reconstruction for discontinuous Galerkin methods on unstructured
grids with a WENOtype linear reconstruction and partial neighboring cells
,
Journal of Computational Physics, v228 (2009), pp.21942212.
 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.375390.
 I. Roy, J.M. Qiu, C.W. Shu and L.Z. Fang,
A WENO algorithm for radiative transfer with resonant scattering
and the Wouthuysenfield coupling
,
New Astronomy, v14 (2009), pp.513520.
 I. Roy, W. Xu, J.M. Qiu, C.W. Shu and L.Z. Fang,
Time evolution of Wouthuysenfield coupling
,
The Astrophysical Journal, v694 (2009), pp.11211130.
 W. Chen, S.C. Wong, C.W. Shu and P. Zhang,
Front tracking algorithm for the LighthillWhithamRichards traffic
flow model with a piecewise quadratic, continuous, nonsmooth, and
nonconcave fundamental diagram
,
International Journal of Numerical Analysis and Modeling,
v6 (2009), pp.562585.
 Y. Lu, S.C. Wong, M. Zhang and C.W. Shu,
The entropy solutions for the LighthillWhithamRichards traffic flow model with a
discontinuous flowdensity relationship
,
Transportation Science, v43 (2009), pp.511530.
 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.503538.
 M. Zhang and C.W. Shu,
Fourier analysis for discontinuous Galerkin and related methods
,
Chinese Science Bulletin, v54 (2009), pp.18091816.
 Z. Xu, Y. Liu and C.W. Shu,
Hierarchical reconstruction for spectral volume method on unstructured grids
,
Journal of Computational Physics, v228 (2009), pp.57875802.
 W. Wang, C.W. Shu, H.C. Yee and B. Sjogreen,
Highorder wellbalanced schemes and applications to nonequilibrium flow
,
Journal of Computational Physics, v228 (2009), pp.66826702.
 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 counterrotating vortices
,
Physics of Fluids, v21 (2009), 076101.
 Y. Cheng, I.M. Gamba, A. Majorana and C.W. Shu,
A discontinuous Galerkin solver for BoltzmannPoisson systems in nano devices
,
Computer Methods in Applied Mechanics and Engineering,
v198 (2009), pp.31303150.
 Y. Xia, S.C. Wong and C.W. Shu,
Dynamic continuum pedestrian flow model with memory effect
,
Physical Review E, v79 (2009), 066113.
 S. Zhang, H. Zhang and C.W. Shu,
Topological structure of shock induced vortex breakdown
,
Journal of Fluid Mechanics, v639 (2009), pp.343372.
 I. Roy, W. Xu, J.M. Qiu, C.W. Shu and L.Z. Fang,
Wouthuysenfield coupling in 21 cm region around highredshift sources
,
The Astrophysical Journal, v703 (2009), pp.19922003.
 J. Cheng and C.W. Shu,
High order schemes for CFD: a review
,
Chinese Journal of Computational Physics, v26 (2009), pp.633655.
 B. Dong and C.W. Shu,
Analysis of a local discontinuous Galerkin method for linear
timedependent fourthorder problems
,
SIAM Journal on Numerical Analysis, v47 (2009), pp.32403268.
 W. Liu, J. Cheng and C.W. Shu,
High order conservative Lagrangian schemes with LaxWendroff
type time discretization for the compressible Euler equations
,
Journal of Computational Physics, v228 (2009), pp.88728891.
 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.27992812.
 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 bidirectional pedestrian
flows
,
Acta Mathematica Scientia, v29B (2009), pp.15411555.
 Y. Xu and C.W. Shu,
Local discontinuous Galerkin methods for highorder timedependent
partial differential equations
,
Communications in Computational Physics, v7 (2010), pp.146.
 Y. Xu and C.W. Shu,
Dissipative numerical methods for the HunterSaxton equation
,
Journal of Computational Mathematics, v28 (2010), pp.606620.
 Y. Xia, Y. Xu and C.W. Shu,
Local discontinuous Galerkin methods for the generalized Zakharov system
,
Journal of Computational Physics, v229 (2010), pp.12381259.
 Y. Cheng and C.W. Shu,
Superconvergence of discontinuous Galerkin and
local discontinuous Galerkin schemes for linear hyperbolic and
convectiondiffusion equations in one space dimension
,
SIAM Journal on Numerical Analysis, v47 (2010), pp.40444072.
 X. Zhang and C.W. Shu,
On maximumprinciplesatisfying high order schemes for scalar conservation laws
,
Journal of Computational Physics, v229 (2010), pp.30913120.
 T. Xiong, M. Zhang, Y.T. Zhang and C.W. Shu,
Fast sweeping fifth order WENO scheme for static HamiltonJacobi
equations with accurate boundary treatment
,
Journal of Scientific Computing, v45 (2010), pp.514536.
 X. Zhang and C.W. Shu,
A genuinely high order total variation diminishing scheme for
onedimensional scalar conservation laws
,
SIAM Journal on Numerical Analysis, v48 (2010), pp.772795.
 Q. Zhang and C.W. Shu,
Stability analysis and a priori error estimates of the third
order explicit RungeKutta discontinuous Galerkin Method for scalar
conservation laws
,
SIAM Journal on Numerical Analysis, v48 (2010), pp.10381063.
 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.604614.
 Y. Liu and C.W. Shu,
Error analysis of the semidiscrete local
discontinuous Galerkin method for semiconductor device simulation models
,
Science China Mathematics, v53 (2010), pp.32553278.
 J. Cheng and C.W. Shu,
A cellcentered Lagrangian scheme with the
preservation of symmetry and conservation properties for
compressible fluid flows in twodimensional cylindrical geometry
,
Journal of Computational Physics, v229 (2010), pp.71917206.
 S. Tan and C.W. Shu,
Inverse LaxWendroff procedure for numerical boundary conditions
of conservation laws
,
Journal of Computational Physics, v229 (2010), pp.81448166.
 C. Wang and C.W. Shu,
An interface treating technique for compressible multimedium
flow with RungeKutta discontinuous Galerkin method
,
Journal of Computational Physics, v229 (2010), pp.88238843.
 X. Zhang and C.W. Shu,
On positivitypreserving high order discontinuous Galerkin schemes
for compressible Euler equations on rectangular meshes
,
Journal of Computational Physics, v229 (2010), pp.89188934.
 Y. Xing, X. Zhang and C.W. Shu,
Positivitypreserving high order wellbalanced discontinuous
Galerkin methods for the shallow water equations
,
Advances in Water Resources, v33 (2010), pp.14761493.
 W. Sun, S.C. Wong, P. Zhang and C.W. Shu,
A shockfitting algorithm for the LighthillWhithamRichards
model on inhomogeneous highways
,
Transportmetrica, v7 (2011), pp.163180.
 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.807827.
 W. Wang, H.C. Yee, B. Sjogreen, T. Magin and C.W. Shu,
Construction of low dissipative highorder wellbalanced filter schemes
for nonequilibrium flows
,
Journal of Computational Physics, v230 (2011), pp.43164335.
 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.2847.
 J.M. Qiu and C.W. Shu,
Conservative high order semiLagrangian finite difference
WENO methods for advection in incompressible flow
,
Journal of Computational Physics, v230 (2011), pp.863889.
 Y. Xing, C.W. Shu and S. Noelle,
On the advantage of wellbalanced schemes for movingwater
equilibria of the shallow water equations
,
Journal of Scientific Computing, v48 (2011), pp.339349.
 T. Xiong, M. Zhang, C.W. Shu, S.C. Wong and P. Zhang,
Highorder computational scheme for a dynamic continuum model for
bidirectional pedestrian flow
,
Computer Aided Civil and Infrastructure Engineering,
v26 (2011), pp.298310.
 Y. Xu and C.W. Shu,
Local discontinuous Galerkin methods for the DegasperisProcesi equation
,
Communications in Computational Physics, v10 (2011), pp.474508.
 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.785806.
 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.216238.
 Y. Cheng, I.M. Gamba, A. Majorana and C.W. Shu,
A brief survey of the discontinuous Galerkin method for
the BoltzmannPoisson equations
,
SEMA Journal, v54 (2011), pp.4764.
 X. Zhang and C.W. Shu,
Positivitypreserving high order discontinuous Galerkin schemes
for compressible Euler equations with source terms
,
Journal of Computational Physics, v230 (2011), pp.12381248.
 J.M. Qiu and C.W. Shu,
Conservative semiLagrangian finite difference WENO formulations with
applications to the Vlasov equation
,
Communications in Computational Physics, v10 (2011), pp.9791000.
 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.318329.
 O. Bokanowski, Y. Cheng and C.W. Shu,
A discontinuous Galerkin solver for front propagation
,
SIAM Journal on Scientific Computing, v33 (2011), pp.923938.
 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.939965.
 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.10091032.
 X. Zhang and C.W. Shu,
Maximumprinciplesatisfying and positivitypreserving highorder
schemes for conservation laws: survey and new developments
,
Proceedings of the Royal Society A, v467 (2011), pp.27522776.
 S. Tan and C.W. Shu,
A high order moving boundary treatment for compressible inviscid flows
,
Journal of Computational Physics, v230 (2011), pp.60236036.
 R. Zhang, M. Zhang and C.W. Shu,
High order positivitypreserving finite volume WENO schemes for a
hierarchical sizestructured population model
,
Journal of Computational and Applied Mathematics, v236 (2011), pp.937949.
 Z. Xu, Y. Liu, H. Du, G. Lin and C.W. Shu,
Pointwise hierarchical reconstruction for discontinuous Galerkin and finite volume
methods for solving conservation laws
,
Journal of Computational Physics, v230 (2011), pp.68436865.
 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.28142827.
 Y. Xing and C.W. Shu,
Highorder finite volume WENO schemes for the shallow
water equations with dry states
,
Advances in Water Resources, v34 (2011), pp.10261038.
 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.18731896.
 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.
 B. Ayuso, J.A. Carrillo and C.W. Shu,
Discontinuous Galerkin methods for the onedimensional VlasovPoisson system
,
CITE>Kinetic and Related Models, v4 (2011), pp.955989.
 J.M. Qiu and C.W. Shu,
Positivity preserving semiLagrangian discontinuous Galerkin
formulation: theoretical analysis and application to the VlasovPoisson system
,
Journal of Computational Physics, v230 (2011), pp.83868409.
 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.
 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.491500.
 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.416446.
 C.W. Shu,
Efficient algorithms for solving partial differential equations
with discontinuous solutions
,
Notices of the American Mathematical Society,
v59 (2012), pp.615621.
Chinese translation in Mathematical Advances in Translation,
v33 (2015), pp.307314.
 J. Cheng and C.W. Shu
Improvement on spherical symmetry in
twodimensional cylindrical coordinates for a class of
control volume Lagrangian schemes
,
Communications in Computational Physics, v11 (2012),
pp.11441168.
 X. Zhang, Y. Xia and C.W. Shu,
Maximumprinciplesatisfying and positivitypreserving
high order discontinuous Galerkin schemes for
conservation laws on triangular meshes
,
Journal of Scientific Computing, v50 (2012), pp.2962.
 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.190214.
 X. Meng, C.W. Shu and B. Wu,
Superconvergence of the local discontinuous Galerkin method
for linear fourthorder timedependent problems in one space dimension
,
IMA Journal of Numerical Analysis, v32 (2012), pp.12941328.
 C. Wang, X. Zhang, C.W. Shu and J. Ning,
Robust high order discontinuous Galerkin schemes
for twodimensional gaseous detonations
,
Journal of Computational Physics, v231 (2012), pp.653665.
 Y. Xu and C.W. Shu,
Optimal error estimates of the semidiscrete local discontinuous
Galerkin methods for high order wave equations
,
SIAM Journal on Numerical Analysis, v50 (2012), pp.79104.
 X. Zhang and C.W. Shu,
A minimum entropy principle of high order schemes
for gas dynamics equations
,
Numerische Mathematik, v121 (2012), pp.545563.
 X. Zhang and C.W. Shu,
Positivitypreserving high order finite difference WENO schemes
for compressible Euler equations
,
Journal of Computational Physics, v231 (2012), pp.22452258.
 S. Tan, C. Wang, C.W. Shu and J. Ning,
Efficient implementation of high order inverse LaxWendroff
boundary treatment for conservation laws
,
Journal of Computational Physics, v231 (2012), pp.25102527.
 X. Zhang, Y. Liu and C.W. Shu,
Maximumprinciplesatisfying high order finite volume
weighted essentially nonoscillatory schemes
for convectiondiffusion equations
,
SIAM Journal on Scientific Computing, v34 (2012), pp.A627A658.
 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.13071328.
 T. Xiong, C.W. Shu and M. Zhang,
WENO scheme with subcell resolution for computing nonconservative
Euler equations with applications to onedimensional compressible
twomedium flows
,
Journal of Scientific Computing, v53 (2012), pp.222247.
 B. Ayuso de Dios, J.A. Carrillo and C.W. Shu,
Discontinuous Galerkin methods for the multidimensional
VlasovPoisson problem
,
Mathematical Models and Methods in Applied Sciences,
v22 (2012), 1250042.
 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.23362356.
 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.31103133.
 C.W. Shu,
On high order accurate weighted essentially nonoscillatory and
discontinuous Galerkin schemes for compressible turbulence simulations
,
Philosophical Transactions of the Royal Society A,
v371 (2013), 20120172.
 X. Zhong and C.W. Shu,
A simple weighted essentially nonoscillatory limiter for
RungeKutta discontinuous Galerkin methods
,
Journal of Computational Physics, v232 (2013), pp.397415.
 Y. Xing and C.W. Shu,
High order wellbalanced WENO scheme for the gas dynamics
equations under gravitational fields
,
Journal of Scientific Computing, v54 (2013), pp.645662.
 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.449464.
 Y. Zhang, X. Zhang and C.W. Shu,
Maximumprinciplesatisfying second order discontinuous Galerkin schemes
for convectiondiffusion equations on triangular meshes
,
Journal of Computational Physics, v234 (2013), pp.295316.
 C. Wang, C.W. Shu, W. Han and J. Ning,
High resolution WENO simulation of 3D detonation waves
,
Combustion and Flame, v160 (2013), pp.447462.
 T. Xiong, C.W. Shu and M. Zhang,
A priori error estimates for semidiscrete discontinuous
Galerkin methods solving
nonlinear HamiltonJacobi equations with smooth solutions
,
International Journal of Numerical
Analysis and Modeling, v10 (2013), pp.154177.
 Y. Yang and C.W. Shu,
Discontinuous Galerkin method for hyperbolic equations
involving $\delta$singularities: negativeorder norm error
estimates and applications
,
Numerische Mathematik, v124, (2013), pp.753781.
 Y. Jiang, C.W. Shu and M. Zhang,
An alternative formulation of finite difference weighted
ENO schemes with LaxWendroff time discretization for conservation laws
,
SIAM Journal on Scientific Computing, v35 (2013), pp.A1137A1160.
 H.C. Yee, D.V. Kotov, W. Wang and C.W. Shu,
Spurious behavior of shockcapturing methods by the fractional
step approach: problems
containing stiff source terms and discontinuities
,
Journal of Computational Physics, v241 (2013), pp.266291.
 X.Y. Hu, N.A. Adams and C.W. Shu,
Positivitypreserving method for highorder conservative
schemes solving compressible Euler equations
,
Journal of Computational Physics, v242 (2013), pp.169180.
 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.967986.
 X. Liu, S. Zhang, H. Zhang and C.W. Shu,
A new class of central compact schemes with
spectrallike resolution I: Linear schemes
,
Journal of Computational Physics, v248 (2013), pp.235256.
 J. Zhu, X. Zhong, C.W. Shu and J.X. Qiu,
RungeKutta discontinuous Galerkin method using a new
type of WENO limiters on unstructured meshes
,
Journal of Computational Physics, v248 (2013), pp.200220.
 S. Zhang, H. Li, X. Liu, H. Zhang and C.W. Shu,
Classification and sound generation of twodimensional
interaction of two Taylor vortices
,
Physics of Fluids, v25 (2013), 056103.
 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.332346.
 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.
 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.109127.
 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.96119.
 J. Lu, C.W. Shu and M. Zhang,
Stability analysis and a priori error estimate of explicit
RungeKutta discontinuous Galerkin methods for correlated random walk
with densitydependent turning rates
,
Science China Mathematics, v56 (2013), pp.26452676.
 C.W. Shu,
Boundpreserving high order accurate schemes
,
Notes of the Canadian Mathematical Society (CMS Notes),
v45 (2013), pp.2425.
 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.
 C.W. Shu,
A brief survey on discontinuous Galerkin methods in
computational fluid dynamics
,
Advances in Mechanics, v43 (2013), pp.541554.
 Y. Jiang, C.W. Shu and M. Zhang,
Freestream preserving finite difference schemes on curvilinear meshes
,
Methods and Applications of Analysis, v21 (2014), pp.130.
 O. Bokanowski, Y. Cheng and C.W. Shu,
A discontinuous Galerkin scheme for front propagation with obstacles
,
Numerische Mathematik, v126 (2014), pp.131.
 Q. Zhang and C.W. Shu,
Error estimates for the third order explicit RungeKutta
discontinuous Galerkin method for linear hyperbolic
equation in onedimension with discontinuous initial data
,
Numerische Mathematik, v126 (2014), pp.703740.
 Z. Chen and C.W. Shu,
Recovering exponential accuracy from collocation point
values of smooth functions with endpoint singularities
conservative schemes
,
Journal of Computational and Applied Mathematics,
v265 (2014), pp.8395.
 J. Cheng and C.W. Shu,
Positivitypreserving Lagrangian scheme for multimaterial
compressible flow
,
Journal of Computational Physics, v257 (2014), pp.143168.
 Y. Zhang, W. Wang, J. Guzman and C.W. Shu,
Multiscale discontinuous Galerkin method for solving elliptic problems
with curvilinear unidirectional rough coefficients
,
Journal of Scientific Computing, v61 (2014), pp.4260.
 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.525540.
 C.S. Chou, C.W. Shu and Y. Xing,
Optimal energy conserving local discontinuous Galerkin
methods for secondorder wave equation in heterogeneous media
,
Journal of Computational Physics, v272 (2014), pp.88107.
 J. Cheng and C.W. Shu,
Second order symmetrypreserving conservative
Lagrangian scheme for compressible Euler equations in
twodimensional cylindrical coordinates
,
Journal of Computational Physics, v272 (2014), pp.245265.
 Y. Xing and C.W. Shu,
A survey of high order schemes for the shallow water equations
,
Journal of Mathematical Study, v47 (2014), pp.221249.
 J. Du, C.W. Shu and M. Zhang,
A simple weighted essentially nonoscillatory limiter for
the correction procedure via reconstruction (CPR) framework
,
Applied Numerical Mathematics, v95 (2015), pp.173198.
 F. Vilar and C.W. Shu,
Development and stability analysis of the inverse LaxWendroff
boundary treatment for central compact schemes
,
ESAIM: Mathematical Modelling and Numerical Analysis
($M^{2}AN$), v49 (2015), pp.3967.
 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.317336.
 H. Wang, C.W. Shu and Q. Zhang,
Stability and error estimates of local discontinuous
Galerkin methods with implicitexplicit timemarching for
advectiondiffusion problems
,
SIAM Journal on Numerical Analysis, v53 (2015), pp.206227.
 X. Meng, C.W. Shu and Y. Yang,
Superconvergence of discontinuous Galerkin methods for
timedependent partial differential equations (in Chinese)
,
Scientia Sinica Mathematica, v45 (2015), pp.10411060.
 J. Du, C.W. Shu and M. Zhang,
A simple weighted essentially nonoscillatory limiter for
the correction procedure via reconstruction (CPR) framework on
unstructured meshes
,
Applied Numerical Mathematics, v90 (2015), pp.146167.
 X. Liu, S. Zhang, H. Zhang and C.W. Shu,
A new class of central compact schemes with spectrallike
resolution II: Hybrid weighted nonlinear schemes
,
Journal of Computational Physics, v284 (2015), pp.133154.
 C. Wang and C.W. Shu,
Progress on highresolution numerical simulation of explosion
mechanics
,
Chinese Science Bulletin (in Chinese), v60 (2015), pp.882898.
 J. Luo, C.W. Shu and Q. Zhang,
A priori error estimates to smooth solutions of the third order
RungeKutta discontinuous
Galerkin method for symmetrizable systems of conservation laws
,
ESAIM:
Mathematical Modelling and Numerical Analysis ($M^{2}AN$), v49 (2015), pp.9911018.
 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.10191046.
 Y. Jiang, C.W. Shu and M. Zhang,
High order finite difference WENO schemes with
positivitypreserving limiter for correlated random walk
with densitydependent turning rates
,
Mathematical Models and Methods in Applied Sciences
($M^3 AS$), v25 (2015), pp.15531588.
 Y. Yang and C.W. Shu,
Analysis of sharp superconvergence of local discontinuous
Galerkin method for onedimensional linear parabolic equations
,
Journal of Computational Mathematics, v33 (2015), pp.323340.
 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.11451165.
 W. Cao, C.W. Shu, Y. Yang and Z. Zhang,
Superconvergence of discontinuous Galerkin methods
for 2D hyperbolic equations
,
SIAM Journal on Numerical Analysis, v53 (2015), pp.16511671.
 C. Wang, X. Dong and C.W. Shu,
Parallel adaptive mesh refinement method based on WENO
finite difference scheme for the simulation of multidimensional
detonation
,
Journal of Computational Physics, v298 (2015), pp.161175.
 J. Du, S.C. Wong, C.W. Shu and M. Zhang,
Reformulating the HoogendoornBovy predictive dynamic
useroptimal model in continuum space with anisotropic condition
,
Transportation Research Part B, v79 (2015), pp.189217.
 X. Meng, C.W. Shu and B. Wu,
Optimal error estimates for discontinuous Galerkin methods based
on upwindbiased fluxes for linear hyperbolic equations
,
Mathematics of Computation, v85 (2016), pp.12251261.
 H. Wang, C.W. Shu and Q. Zhang,
Stability analysis and error estimates of
local discontinuous Galerkin methods
with implicitexplicit timemarching
for nonlinear convectiondiffusion problems
,
Applied Mathematics and Computation, v272 (2016), pp.237258.
 B. Dong, C.W. Shu and W. Wang,
A new multiscale discontinuous Galerkin method for
the onedimensional stationary Schr\"{o}dinger equation
,
Journal of Scientific Computing, v66 (2016), pp.321345.
 O. Bokanowski, Y. Cheng and C.W. Shu,
Convergence of discontinuous Galerkin schemes for front
propagation with obstacles
,
Mathematics of Computation, v85 (2016), pp.21312159.
 Y. Liu and C.W. Shu,
Analysis of the local discontinuous Galerkin method for
the driftdiffusion model of semiconductor devices
,
Science China Mathematics, v59 (2016), pp.115140.
 J. Zhu, X. Zhong, C.W. Shu and J.X. Qiu,
RungeKutta discontinuous Galerkin method with a
simple and compact Hermite WENO limiter
,
Communications in Computational Physics,
v19 (2016), pp.944969.
 H. Wang, S. Wang, C.W. Shu and Q. Zhang,
Local discontinuous Galerkin methods with implicitexplicit
timemarching for multidimensional convectiondiffusion problems
,
ESAIM:
Mathematical Modelling and Numerical Analysis ($M^{2}AN$),
v50 (2016), pp.10831105.
 T. Li, C.W. Shu and M. Zhang,
Stability analysis of the inverse LaxWendroff boundary
treatment for high order upwindbiased finite difference schemes
,
Journal of Computational and Applied Mathematics,
v299 (2016), pp.140158.
 L. Wu, Y.T. Zhang, S. Zhang and C.W. Shu,
High order fixedpoint sweeping WENO methods for steady state
of hyperbolic conservation laws and its convergence study
,
Communications in Computational Physics,
v20 (2016), pp.835869.
 T. Qin, C.W. Shu and Y. Yang,
Boundpreserving discontinuous Galerkin methods
for relativistic hydrodynamics
,
Journal of Computational Physics, v315 (2016), pp.323347.
 F. Vilar, C.W. Shu and P.H. Maire,
Positivitypreserving cellcentered Lagrangian schemes for
multimaterial compressible flows: From firstorder to highorders.
Part I: The onedimensional case
,
Journal of Computational Physics, v312 (2016), pp.385415.
 F. Vilar, C.W. Shu and P.H. Maire,
Positivitypreserving cellcentered Lagrangian schemes for
multimaterial compressible flows: From firstorder to highorders.
Part II: The twodimensional case
,
Journal of Computational Physics, v312 (2016), pp.416442.
 C.W. Shu,
High order WENO and DG methods for timedependent
convectiondominated PDEs: a brief survey of several
recent developments
,
Journal of Computational Physics, v316 (2016), pp.598613.
 J. Lu, J. Fang, S. Tan, C.W. Shu and M. Zhang,
Inverse LaxWendroff procedure for numerical boundary
conditions of convectiondiffusion equations
,
Journal of Computational Physics, v317 (2016), pp.276300.
 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.A3094A3128.
 D. Yuan, J. Cheng and C.W. Shu,
High order positivitypreserving discontinuous
Galerkin methods for radiative transfer equations
,
SIAM Journal on Scientific Computing, v38 (2016), pp.A2987A3019.
 C. Wang, J. Ding, C.W. Shu and T. Li,
Threedimensional high order largescale numerical
investigation on the air explosion
,
Computers and Fluids, v137 (2016), pp.7079.
 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.780804.
 Z. Sun and C.W. Shu,
Stability analysis and error estimates of LaxWendroff
discontinuous Galerkin methods for linear conservation laws
,
ESAIM: Mathematical Modelling and Numerical
Analysis ($M^{2}AN$), v51 (2017), pp.10631087.
 T. Li, C.W. Shu and M. Zhang,
Stability analysis of the inverse
LaxWendroff boundary treatment for high order central
difference schemes for diffusion equations
,
Journal of Scientific Computing, v70 (2017), pp.576607.
 J. Huang and C.W. Shu,
Error estimates to smooth solutions of semidiscrete
discontinuous Galerkin methods with quadrature rules for
scalar conservation laws
,
Numerical Methods for Partial Differential Equations,
v33 (2017), pp.467488.
 J. Zhu, X. Zhong, C.W. Shu and J. Qiu,
RungeKutta discontinuous Galerkin method with a simple
and compact Hermite WENO limiter on unstructured meshes
,
Communications in Computational Physics, v21 (2017), pp.623649.
 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.17331771.
 H. Shen, C.Y. Wen, M. Parsani and C.W. Shu,
Maximumprinciplesatisfying spacetime conservation
element and solution element scheme applied to compressible
multifluids
,
Journal of Computational Physics, v330 (2017), pp.668692.
 Z. Sun and C.W. Shu,
Stability of the fourth order RungeKutta method for
timedependent partial differential equations
,
Annals of Mathematical Sciences and Applications,
v2 (2017), pp.255284.
 J. Huang and C.W. Shu,
A secondorder asymptoticpreserving and positivepreserving
discontinuous Galerkin scheme for the KerrDebye model
,
Mathematical Models and Methods in Applied
Sciences, v27 (2017), pp.549–579.
 X.H. Li, C.W. Shu and Y. Yang,
Local discontinuous Galerkin method for the KellerSegel
chemotaxis model
,
Journal of Scientific Computing, v73 (2017),
pp.943967.
 G. Fu and C.W. Shu,
Analysis of an embedded discontinuous Galerkin method
with implicitexplicit timemarching for convectiondiffusion
problems
,
International Journal of Numerical
Analysis and Modeling, v14 (2017), pp.477499.
 C.Y. Lam and C.W. Shu,
A phasebased interior penalty discontinuous Galerkin method
for the Helmholtz equation with spatially varying wavenumber
,
Computer Methods in Applied Mechanics and
Engineering, v318 (2017), pp.456473.
 F. Zheng, C.W. Shu and J. Qiu,
Finite difference Hermite WENO schemes for
the HamiltonJacobi equations
,
Journal of Computational Physics, v337 (2017), pp.2741.
 J. Li, C. Shi and C.W. Shu,
Optimal nondissipative discontinuous Galerkin methods for
Maxwell's equations in Drude metamaterials
,
Computers and Mathematics with Applications, v73 (2017), pp.17601780.
 Y. Liu, Y. Cheng and C.W. Shu,
A simple boundpreserving sweeping technique for
conservative numerical approximations
,
Journal of Scientific Computing, v73 (2017), pp.10281071.
 H. Wang, Q. Zhang and C.W. Shu,
Stability analysis and error estimates of local discontinuous
Galerkin methods with implicitexplicit timemarching for the
timedependent fourth order PDEs
,
ESAIM: Mathematical Modelling and Numerical
Analysis ($M^{2}AN$), v51 (2017), pp.19311955.
 Q. Liu, C.W. Shu and M. Zhang,
Discontinuous Galerkin methods for weakly coupled hyperbolic
multidomain problems
,
SIAM Journal on Scientific Computing,
v321 (2017), pp.209234.
 J. MoralesEscalante, I.M. Gamba, Y. Cheng, A. Majorana,
C.W. Shu and J. Chelikowsky,
Discontinuous Galerkin deterministic solvers for a
BoltzmannPoisson model of hot electron transport byaveraged empirical pseudopotential band structures
,
Computer Methods in Applied Mechanics and Engineering,
v321 (2017), pp.209234.
 W. Cao, C.W. Shu and Z. Zhang,
Superconvergence of discontinuous Galerkin methods for
1D linear hyperbolic equations with degenerate variable coefficients
,
ESAIM: Mathematical Modelling and Numerical
Analysis ($M^{2}AN$), v51 (2017), pp.22132235.
 J. Du and C.W. Shu,
Positivitypreserving highorder schemes for conservation laws
on arbitrarily distributed point clouds with a simple WENO limiter
,
International Journal of Numerical
Analysis and Modeling, v15 (2018), pp.125.
 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.427461.
 C. Shi and C.W. Shu, `
On local conservation of numerical methods for conservation laws
,
Computers and Fluids, to appear.
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Local discontinuous Galerkin methods with implicitexplicit
timemarching for timedependent incompressible fluid flow
,
Mathematics of Computation, to appear.
 G. Fu and C.W. Shu,
A new troublecell indicator for discontinuous Galerkin
methods for hyperbolic conservation laws
,
Journal of Computational Physics, v347 (2017),
pp.305327.
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Unconditional energy stability analysis of a second order
implicitexplicit
local discontinuous Galerkin method for the CahnHilliard equation
,
Journal of Scientific Computing, v73 (2017), pp.11781203.
 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.8096.
 D. Ling, J. Cheng and C.W. Shu,
Positivitypreserving and symmetrypreserving Lagrangian
schemes for compressible Euler equations in cylindrical coordinates,
,
Computers and Fluids, v157 (2017), pp.112130.
 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.76104.
 T. Qin and C.W. Shu,
Implicit positivitypreserving high order discontinuous
Galerkin methods for conservation laws
,
SIAM Journal on Scientific Computing, to appear.
 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.163178.
 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, to appear.
 W. Cao, C.W. Shu, Y. Yang and Z. Zhang,
Superconvergence of discontinuous Galerkin method
for nonlinear hyperbolic equations
potentials
,
SIAM Journal on Numerical Analysis, to appear.
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A new class of nonoscillatory discontinuous Galerkin
finite element methods for conservation laws,
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Finite Element Methods in Flow Problems, UAH Press, 1989,
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Essentially NonOscillatory methods for twodimensional
hydrodynamic models, in Proceedings of
the International
Workshop on Computational Electronics, Beckman Institute,
University of Illinois, May 1992, pp.8386.
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The ENO method for the hydrodynamic model for semiconductor
devices, in High
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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.227234.
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Energy models for onecarrier transport in
semiconductor devices, in IMA
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Transport effect, hyperbolicity, and shock capturing algorithms
for device simulations, in Proceedings
of the Third
International Workshop on Computational Electronics, Portland,
Oregon, May 1820, 1994, pp.252255.
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The resolution of the Gibbs phenomenon,
ICASE Research Quarterly, Vol. 3, No. 2, June 1994, pp.57.
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Essentially nonoscillatory 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
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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.169187.
 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. 38353846.
 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. 131138.
 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.356362.
 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 (IWCE6), Osaka University, Japan,
October 1921, 1998, IEEE Catalog Number 98EX116.
 C.W. Shu,
Essentially nonoscillatory and weighted essentially nonoscillatory 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.325432.
 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.103140.
 C.W. Shu,
High order ENO and WENO schemes for computational fluid dynamics,
in HighOrder Methods for Computational Physics,
T.J. Barth and H. Deconinck, editors,
Lecture Notes in Computational Science and Engineering, volume 9,
Springer, 1999, pp.439582.
 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.350.
 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.147156.
 B. Cockburn, M. Luskin, C.W. Shu and E. Suli,
Postprocessing 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.291300.
 C. Hu, O. Lepsky and C.W. Shu,
The effect of least square procedure for discontinuous Galerkin
methods for HamiltonJacobi 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.343348.
 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.369374.
 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.144155.
 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.5165.
 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, SpringerVerlag, New York, 2003, pp.7584.
 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, SpringerVerlag,
Berlin, 2003, pp.7988.
 Y.T. Zhang and C.W. Shu,
Third and fourth order weighted ENO schemes for
HamiltonJacobi equations on 2D unstructured meshes
,
in Hyperbolic Problems: Theory, Numerics,
Applications, T.Y. Hou and E. Tadmor, editors, SpringerVerlag,
Berlin, 2003, pp.941950.
 L.L. Feng, C.W. Shu and M. Zhang,
A hybrid cosmological hydrodynamic/Nbody code based on
the weighted essentially nonoscillatory scheme
,
Proceedings of the Fifth SinoGermany 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) p1823.
 Y.T. Zhang, J. Shi, C.W. Shu and Y. Zhou,
Resolution of high order WENO schemes and NavierStokes
simulation of the RayleighTaylor 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 1720, 2003, volume 1,
pp.12161218, Elsevier Science.
 B. Cockburn, F. Li and C.W. Shu,
Discontinuous Galerkin methods for equations with
divergencefree 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 1720, 2003, volume 2,
pp.19001902, Elsevier Science.
 S. Chen, W. E and C.W. Shu,
The heterogeneous multiscale 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.10721075.
 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.151171.
 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.4056.
 C.W. Shu,
High order numerical methods for time dependent HamiltonJacobi 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.4791.
 Y. Xia, L. Huang, S.C. Wong, M. Zhang, C.W. Shu and W.H.K. Lam,
The followthecrowd 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.309317.
 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.6373.
 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.149201.
 S. Noelle, Y. Xing and C.W. Shu,
Highorder wellbalanced schemes
,
Numerical Methods for Balance Laws,
G. Puppo and G. Russo, editors,
Quaderni di Matematica, volume 24, Seconda Universita di
Napoli, 2009, pp.166.
 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.661668.
 J.W. Jerome, M.A. Ratner, J.D. Servaites, C.W. Shu and S. Tan,
Simulation of the BuxtonClarke model for organic photovoltaic cells
,
in Proceedings of the 14th International Workshop on Computational
Electronics, IWCE, 2629
October, 2010, Pisa, Italy. Pisa University Press, pp.195198.
 Y. Cheng, I.M. Gamba, A. Majorana and C.W. Shu,
Discontinuous Galerkin methods for
the BoltzmannPoisson systems in semiconductor device simulations
,
AIP Conference Proceedings, volume 1333, 2011, pp.890895.
 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.747758.
 S. Tan and C.W. Shu,
Inverse LaxWendroff 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.4163.
 C.W. Shu,
Survey on discontinuous Galerkin methods for HamiltonJacobi
equations
,
Proceedings of the Eighth International Conference on
Scientific Computing and Applications,
Contemporary Mathematics, American Mathematical Society,
volume 586, 2013, pp.323330.
 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. VazquezCendon, A. Hidalgo, P. GarciaNavarro and
L. Cea, editors, CRC Press, Taylor and Francis Group, London,
2013, pp.919.
 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.2562.
 C.W. Shu,
Discontinuous Galerkin methods: Time dependent problems
,
Encyclopedia of Applied and Computational Mathematics,
Bjorn Engquist, Editor,
SpringerVerlag, BerlinHeidelberg, 2015, pp.365367.
 C.W. Shu,
Error estimates for linear hyperbolic equations
,
Encyclopedia of Applied and Computational Mathematics,
Bj\"{o}rn Engquist, Editor,
SpringerVerlag, BerlinHeidelberg, 2015, pp.440445.
 S. Zhang, X. Liu, H. Zhang and C.W. Shu,
High order and high resolution numerical schemes for
computational aeroacoustics and their applications
,
in FluidStructureSound Interactions and Control,
Y. Zhou et al, Editors,
Lecture Notes in Mechanical Engineering,
Springer, BerlinHeidelberg, 2016, pp.2732.
 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,
BeijingBoston, 2016, pp.681689.
 C.W. Shu,
Discontinuous Galerkin methods for timedependent
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.369397.
 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,
NorthHolland, Elsevier, Amsterdam, 2016, pp.103122.
 C.W. Shu and S. Tan,
Inverse LaxWendroff 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,
NorthHolland, Elsevier, Amsterdam, 2017, pp.2352.
 C.W. Shu,
Boundpreserving high order finite volume schemes for
conservation laws and convectiondiffusion 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.314.
 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. 0200061  0200063, doi: 10.1063/1.4992152
 C.W. Shu,
RungeKutta and LaxWendroff 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. 3200101  3200103, doi: 10.1063/1.4992491
 C.W. Shu,
A brief survey on high order numerical methods for
convection dominated problems
,
to appear in Proceedings of the 6th International Congress of
Chinese Mathematicians, Higher Education Press and International
Press, ALM 36, pp.119133.
 C.W. Shu,
Boundpreserving high order schemes for hyperbolic equations:
survey and recent developments
,
submitted to the Proceedings of the Sixteenth International
Conference on Hyperbolic Problems (Hyp2016),
Springer Proceedings in Mathematics and Statistics, Springer.
 V. Kucera and C.W. Shu,
On the time growth of the error of the DG method for
advective problems
,
submitted to IMA Journal of Numerical Analysis.
 F. Filbet and C.W. Shu,
DiscontinuousGalerkin methods for a kinetic model
of selforganized dynamics potentials
,
submitted to Mathematical Models and Methods in Applied
Sciences ($M^3 AS$).
 J. Huang and C.W. Shu,
Boundpreserving modified exponential RungeKutta
discontinuous Galerkin methods
for scalar conservation laws with stiff source terms
,
submitted to Journal of Computational Physics.
 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
,
submitted to Shock Waves.