Edit Profile (opens in new tab) Shu, Chi-Wang Compute Distance To: Compute Author ID: shu.chi-wang Published as: Shu, Chi-Wang; Shu, Chiwang; Shu, C.-W.; Shu, C.; Shu, Chi-wang Further Spellings: 舒其望 Homepage: https://www.dam.brown.edu/people/shu/ External Links: MGP · Wikidata · Google Scholar · ResearchGate · dblp · GND · IdRef · theses.fr Documents Indexed: 419 Publications since 1987, including 3 Books 22 Contributions as Editor Biographic References: 1 Publication Co-Authors: 247 Co-Authors with 410 Joint Publications 8,860 Co-Co-Authors all top 5 Co-Authors 26 single-authored 41 Zhang, Mengping 21 Qiu, Jianxian 20 Cheng, Juan 20 Xu, Yan 19 Zhang, Qiang 16 Cockburn, Bernardo 14 Gottlieb, David I. 13 Xing, Yulong 13 Zhang, Yongtao 13 Zhu, Jun 11 Carrillo de la Plata, José Antonio 11 Cheng, Yingda 11 Martínez Gamba, Irene 11 Zhang, Shuhai 11 Zhang, Xiangxiong 10 Wang, Wei 9 Wang, Haijin 9 Xia, Yinhua 9 Yang, Yang 8 Liu, Yingjie 7 E, Weinan 7 Lu, Jianfang 6 Amat, Sergio P. 6 Gottlieb, Sigal 6 Jerome, Joseph W. 6 Li, Fengyan 6 Majorana, Armando 6 Osher, Stanley Joel 6 Sun, Zheng 6 Tadmor, Eitan 6 Tan, Sirui 6 Wong, Sze Chun 5 Hu, Changqing 5 Huang, Juntao 5 Liu, Yunxian 5 Meng, Xiong 5 Qiu, Jingmei 5 Ryan, Jennifer K. 5 Xu, Zhiliang 5 Yee, Helen C. 4 Abgrall, Rémi 4 Cheng, Shiu-Yuen 4 Chou, Ching-Shan 4 Du, Jie 4 Fu, Guosheng 4 Hesthaven, Jan S. 4 Li, Jichun 4 Sjogreen, Bjorn 4 Wu, Kailiang 4 Xiong, Tao 4 Xu, Zhengfu 4 Zhang, Zhimin 4 Zhong, Xinghui 3 Bokanowski, Olivier 3 Cai, Wei 3 Cao, Waixiang 3 Chen, Shanqin 3 Chen, Tianheng 3 Dong, Bo 3 Filbet, Francis 3 Guo, Yan 3 Guzmán, Johnny 3 Jiang, Shufen 3 Jiang, Yan 3 Kang, Ming-Chang 3 Karniadakis, George Em 3 Li, Tingting 3 Ling, Dan 3 Liu, Kefeng 3 Liu, Yuan 3 Noelle, Sebastian 3 Shi, Cengke 3 Tang, Shanjian 3 Tao, Qi 3 Vilar, François 3 Wu, Boying 3 Yan, Jue 3 Yang, Lo 3 Yau, Shing-Tung 3 Zhang, Hanxin 3 Zheng, Feng 3 Zhou, Tie 2 Atkins, Harold L. 2 Balsara, Dinshaw S. 2 Carpenter, Mark H. 2 Cercignani, Carlo 2 Chen, Yanlai 2 Chen, Zheng 2 Dumbser, Michael 2 Erlebacher, Gordon 2 Fang, Jinwei 2 Jiang, Guangshan 2 Ketcheson, David I. 2 Kotov, Dmitry V. 2 Kučera, Václav 2 Lam, William H. K. 2 Lei, Nuo 2 Lepsky, Olga 2 Levy, Doron 2 Li, Yue ...and 148 more Co-Authors all top 5 Serials 104 Journal of Computational Physics 42 Journal of Scientific Computing 29 SIAM Journal on Numerical Analysis 24 SIAM Journal on Scientific Computing 21 Communications in Computational Physics 15 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 14 Mathematics of Computation 11 Computer Methods in Applied Mechanics and Engineering 9 Journal of Computational and Applied Mathematics 8 Computers and Fluids 8 Numerische Mathematik 8 Applied Numerical Mathematics 8 Communications on Applied Mathematics and Computation 7 Journal of Computational Mathematics 7 International Journal of Numerical Analysis and Modeling 6 Science China. Mathematics 5 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 5 Methods and Applications of Analysis 4 Physica D 4 Physics of Fluids 3 IMA Journal of Numerical Analysis 3 SIAM Review 3 Multiscale Modeling & Simulation 2 Computers & Mathematics with Applications 2 Journal of Fluid Mechanics 2 Transport Theory and Statistical Physics 2 Applied Mathematics and Computation 2 International Journal for Numerical Methods in Engineering 2 Quarterly of Applied Mathematics 2 Acta Mathematicae Applicatae Sinica. English Series 2 Applied Mathematics Letters 2 Contemporary Mathematics 2 Handbook of Numerical Analysis 2 Kinetic and Related Models 2 Advances in Applied Mathematics and Mechanics 2 Annals of Mathematical Sciences and Applications 1 AIAA Journal 1 International Journal for Numerical Methods in Fluids 1 Nonlinearity 1 Physics of Fluids, A 1 Mathematica Numerica Sinica 1 SIAM Journal on Scientific and Statistical Computing 1 RAIRO. Modélisation Mathématique et Analyse Numérique 1 Numerical Methods for Partial Differential Equations 1 Applied Mathematical Modelling 1 SIAM Journal on Applied Mathematics 1 SIAM Journal on Mathematical Analysis 1 Notices of the American Mathematical Society 1 Chinese Science Bulletin 1 Advances in Computational Mathematics 1 Engineering Analysis with Boundary Elements 1 International Journal of Computational Fluid Dynamics 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Journal of Mathematical Study 1 Discrete and Continuous Dynamical Systems. Series B 1 Acta Mathematica Scientia. Series B. (English Edition) 1 Lecture Notes in Mathematics 1 Lecture Notes in Computational Science and Engineering 1 Acta Mechanica Sinica 1 Inverse Problems and Imaging 1 Scientia Sinica. Mathematica 1 S\(\vec{\text{e}}\)MA Journal 1 Boletín de la Sociedad Española de Matemática Aplicada. S\(\vec{\text{e}}\)MA 1 Stochastic and Partial Differential Equations. Analysis and Computations 1 Advanced Courses in Mathematics – CRM Barcelona all top 5 Fields 360 Numerical analysis (65-XX) 232 Partial differential equations (35-XX) 155 Fluid mechanics (76-XX) 28 Statistical mechanics, structure of matter (82-XX) 16 General and overarching topics; collections (00-XX) 10 Calculus of variations and optimal control; optimization (49-XX) 9 Harmonic analysis on Euclidean spaces (42-XX) 9 Biology and other natural sciences (92-XX) 8 Probability theory and stochastic processes (60-XX) 8 Mechanics of deformable solids (74-XX) 8 Optics, electromagnetic theory (78-XX) 7 Classical thermodynamics, heat transfer (80-XX) 7 Operations research, mathematical programming (90-XX) 6 History and biography (01-XX) 5 Special functions (33-XX) 5 Ordinary differential equations (34-XX) 5 Approximations and expansions (41-XX) 4 Astronomy and astrophysics (85-XX) 3 Group theory and generalizations (20-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Differential geometry (53-XX) 3 Computer science (68-XX) 3 Mechanics of particles and systems (70-XX) 2 Nonassociative rings and algebras (17-XX) 2 Topological groups, Lie groups (22-XX) 2 Integral equations (45-XX) 1 Combinatorics (05-XX) 1 Number theory (11-XX) 1 Associative rings and algebras (16-XX) 1 Real functions (26-XX) 1 Relativity and gravitational theory (83-XX) 1 Geophysics (86-XX) 1 Systems theory; control (93-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 381 Publications have been cited 22,453 times in 7,168 Documents Cited by ▼ Year ▼ Efficient implementation of weighted ENO schemes. Zbl 0877.65065Jiang, Guang-Shan; Shu, Chi-Wang 1,601 1996 Efficient implementation of essentially nonoscillatory shock-capturing schemes. Zbl 0653.65072Shu, Chi-Wang; Osher, Stanley 1,489 1988 The local discontinuous Galerkin method for time-dependent convection-diffusion systems. Zbl 0927.65118Cockburn, Bernardo; Shu, Chi-Wang 886 1998 Efficient implementation of essentially nonoscillatory shock-capturing schemes. II. Zbl 0674.65061Shu, Chi-Wang; Osher, Stanley 833 1989 TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. II: General framework. Zbl 0662.65083Cockburn, Bernardo; Shu, Chi-Wang 817 1989 The Runge-Kutta discontinuous Galerkin method for conservation laws. I: Multidimensional systems. Zbl 0920.65059Cockburn, Bernardo; Shu, Chi-Wang 749 1998 Strong stability-preserving high-order time discretization methods. Zbl 0967.65098Gottlieb, Sigal; Shu, Chi-Wang; Tadmor, Eitan 736 2001 Runge–Kutta discontinuous Galerkin methods for convection-dominated problems. Zbl 1065.76135Cockburn, Bernardo; Shu, Chi-Wang 658 2001 TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. III: One-dimensional systems. Zbl 0677.65093Cockburn, Bernardo; Lin, San-Yih; Shu, Chi-Wang 564 1989 The Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. IV: The multidimensional case. Zbl 0695.65066Cockburn, Bernardo; Hou, Suchung; Shu, Chi-Wang 559 1990 Total variation diminishing Runge-Kutta schemes. Zbl 0897.65058Gottlieb, Sigal; Shu, Chi-Wang 542 1998 Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws. Zbl 0927.65111Shu, Chi-Wang 449 1998 Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy. Zbl 0961.65078Balsara, Dinshaw S.; Shu, Chi-Wang 401 2000 Total-variation-diminishing time discretizations. Zbl 0662.65081Shu, Chiwang 341 1988 High order weighted essentially nonoscillatory schemes for convection dominated problems. Zbl 1160.65330Shu, Chi-Wang 322 2009 Weighted essentially non-oscillatory schemes on triangular meshes. Zbl 0926.65090Hu, Changqing; Shu, Chi-Wang 310 1999 The development of discontinuous Galerkin methods. Zbl 0989.76045Cockburn, Bernardo; Karniadakis, George E.; Shu, Chi-Wang 290 2000 High-order essentially nonoscillatory schemes for Hamilton-Jacobi equations. Zbl 0736.65066Osher, Stanley; Shu, Chi-Wang 246 1991 The Runge-Kutta local projection \(P^ 1\)-discontinuous-Galerkin finite element method for scalar conservation laws. Zbl 0732.65094Cockburn, Bernardo; Shu, Chi-Wang 238 1991 On positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations on rectangular meshes. Zbl 1282.76128Zhang, Xiangxiong; Shu, Chi-Wang 221 2010 On the Gibbs phenomenon and its resolution. Zbl 0885.42003Gottlieb, David; Shu, Chi-Wang 220 1997 On maximum-principle-satisfying high order schemes for scalar conservation laws. Zbl 1187.65096Zhang, Xiangxiong; Shu, Chi-Wang 212 2010 A local discontinuous Galerkin method for KdV type equations. Zbl 1021.65050Yan, Jue; Shu, Chi-Wang 172 2002 Runge-Kutta discontinuous Galerkin method using WENO limiters. Zbl 1077.65109Qiu, Jianxian; Shu, Chi-Wang 166 2005 A technique of treating negative weights in WENO schemes. Zbl 0992.65094Shi, Jing; Hu, Changqing; Shu, Chi-Wang 165 2002 Hermite WENO schemes and their application as limiters for Runge-Kutta discontinuous Galerkin method: One-dimensional case. Zbl 1039.65068Qiu, Jianxian; Shu, Chi-Wang 159 2004 Strong stability preserving Runge-Kutta and multistep time discretizations. Zbl 1241.65064Gottlieb, Sigal; Ketcheson, David; Shu, Chi-Wang 138 2011 Maximum-principle-satisfying and positivity-preserving high-order schemes for conservation laws: survey and new developments. Zbl 1222.65107Zhang, Xiangxiong; Shu, Chi-Wang 136 2011 TVB uniformly high-order schemes for conservation laws. Zbl 0628.65075Shu, Chiwang 136 1987 High order finite difference WENO schemes with the exact conservation property for the shallow water equations. Zbl 1114.76340Xing, Yulong; Shu, Chi-Wang 132 2005 Hermite WENO schemes and their application as limiters for Runge-Kutta discontinuous Galerkin method. II: Two dimensional case. Zbl 1134.65358Qiu, Jianxian; Shu, Chi-Wang 127 2005 Locally divergence-free discontinuous Galerkin methods for the Maxwell equations. Zbl 1049.78019Cockburn, Bernardo; Li, Fengyan; Shu, Chi-Wang 118 2004 Local discontinuous Galerkin methods for high-order time-dependent partial differential equations. Zbl 1364.65205Xu, Yan; Shu, Chi-Wang 113 2010 High order strong stability preserving time discretizations. Zbl 1203.65135Gottlieb, Sigal; Ketcheson, David I.; Shu, Chi-Wang 113 2009 Local discontinuous Galerkin methods for nonlinear Schrödinger equations. Zbl 1072.65130Xu, Yan; Shu, Chi-Wang 111 2005 Resolution of high order WENO schemes for complicated flow structures. Zbl 1047.76081Shi, Jing; Zhang, Yong-Tao; Shu, Chi-Wang 105 2003 On the construction, comparison, and local characteristic decomposition for high-order central WENO schemes. Zbl 1018.65106Qiu, Jianxian; Shu, Chi-Wang 104 2002 High-order well-balanced finite volume WENO schemes for shallow water equation with moving water. Zbl 1120.76046Noelle, Sebastian; Xing, Yulong; Shu, Chi-Wang 103 2007 High order well-balanced finite volume WENO schemes and discontinuous Galerkin methods for a class of hyperbolic systems with source terms. Zbl 1089.65091Xing, Yulong; Shu, Chi-Wang 100 2006 High-order finite difference and finite volume WENO schemes and discontinuous Galerkin methods for CFD. Zbl 1034.76044Shu, Chi-Wang 97 2003 Error estimates to smooth solutions of Runge-Kutta discontinuous Galerkin methods for scalar conservation laws. Zbl 1078.65080Zhang, Qiang; Shu, Chi-Wang 94 2004 Maximum-principle-satisfying and positivity-preserving high order discontinuous Galerkin schemes for conservation laws on triangular meshes. Zbl 1247.65131Zhang, Xiangxiong; Xia, Yinhua; Shu, Chi-Wang 93 2012 Runge-Kutta discontinuous Galerkin method using WENO limiters II: Unstructured meshes. Zbl 1157.65453Zhu, Jun; Qiu, Jianxian; Shu, Chi-Wang; Dumbser, Michael 92 2008 A discontinuous Galerkin finite element method for Hamilton-Jacobi equations. Zbl 0946.65090Hu, Changqing; Shu, Chi-Wang 87 1999 Local discontinuous Galerkin methods for partial differential equations with higher order derivatives. Zbl 1003.65115Yan, Jue; Shu, Chi-Wang 86 2002 High-order WENO schemes for Hamilton-Jacobi equations on triangular meshes. Zbl 1034.65051Zhang, Yong-Tao; Shu, Chi-Wang 86 2003 On a cell entropy inequality for discontinuous Galerkin methods. Zbl 0801.65098Jiang, Guangshan; Shu, Chi-Wang 83 1994 A comparison of troubled-cell indicators for Runge-Kutta discontinuous Galerkin methods using weighted essentially nonoscillatory limiters. Zbl 1092.65084Qiu, Jianxian; Shu, Chi-Wang 82 2005 Positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations with source terms. Zbl 1391.76375Zhang, Xiangxiong; Shu, Chi-Wang 82 2011 An efficient class of WENO schemes with adaptive order. Zbl 1422.65146Balsara, Dinshaw S.; Garain, Sudip; Shu, Chi-Wang 81 2016 Superconvergence of discontinuous Galerkin and local discontinuous Galerkin schemes for linear hyperbolic and convection-diffusion equations in one space dimension. Zbl 1208.65137Cheng, Yingda; Shu, Chi-Wang 80 2010 Positivity-preserving high order finite difference WENO schemes for compressible Euler equations. Zbl 1426.76493Zhang, Xiangxiong; Shu, Chi-Wang 78 2012 A high-order ENO conservative Lagrangian type scheme for the compressible Euler equations. Zbl 1126.76035Cheng, Juan; Shu, Chi-Wang 77 2007 A discontinuous Galerkin finite element method for time dependent partial differential equations with higher order derivatives. Zbl 1141.65075Cheng, Yingda; Shu, Chi-Wang 77 2008 Enhanced accuracy by post-processing for finite element methods for hyperbolic equations. Zbl 1015.65049Cockburn, Bernardo; Luskin, Mitchell; Shu, Chi-Wang; Süli, Endre 76 2003 Local discontinuous Galerkin methods for the Cahn-Hilliard type equations. Zbl 1131.65088Xia, Yinhua; Xu, Yan; Shu, Chi-Wang 74 2007 On the Gibbs phenomenon. I: Recovering exponential accuracy from the Fourier partial sum of a nonperiodic analytic function. Zbl 0781.42022Gottlieb, David; Shu, Chi-Wang; Solomonoff, Alex; Vandeven, Hervé 73 1992 On positivity preserving finite volume schemes for Euler equations. Zbl 0857.76062Perthame, Benoit; Shu, Chi-Wang 72 1996 Entropy stable high order discontinuous Galerkin methods with suitable quadrature rules for hyperbolic conservation laws. Zbl 1380.65253Chen, Tianheng; Shu, Chi-Wang 72 2017 Third order WENO scheme on three dimensional tetrahedral meshes. Zbl 1364.65177Zhang, Yong-Tao; Shu, Chi-Wang 72 2009 Runge-Kutta discontinuous Galerkin method using a new type of WENO limiters on unstructured meshes. Zbl 1349.65501Zhu, Jun; Zhong, Xinghui; Shu, Chi-Wang; Qiu, Jianxian 71 2013 A local discontinuous Galerkin method for the Camassa-Holm equation. Zbl 1173.65063Xu, Yan; Shu, Chi-Wang 71 2008 Stability analysis and a priori error estimates of the third order explicit Runge-Kutta discontinuous Galerkin method for scalar conservation laws. Zbl 1217.65178Zhang, Qiang; Shu, Chi-Wang 69 2010 High order ENO and WENO schemes for computational fluid dynamics. Zbl 0937.76044Shu, Chi-Wang 68 1999 Central discontinuous Galerkin methods on overlapping cells with a nonoscillatory hierarchical reconstruction. Zbl 1157.65450Liu, Yingjie; Shu, Chi-Wang; Tadmor, Eitan; Zhang, Mengping 68 2007 Local discontinuous Galerkin methods for nonlinear dispersive equations. Zbl 1055.65109Levy, Doron; Shu, Chi-Wang; Yan, Jue 67 2004 Analysis of optimal superconvergence of discontinuous Galerkin method for linear hyperbolic equations. Zbl 1276.65055Yang, Yang; Shu, Chi-Wang 66 2012 Small-scale structures in Boussinesq convection. Zbl 0822.76087E, Weinan; Shu, Chi-Wang 64 1994 Error estimates of the semi-discrete local discontinuous Galerkin method for nonlinear convection-diffusion and KdV equations. Zbl 1173.65338Xu, Yan; Shu, Chi-Wang 63 2007 Positivity-preserving method for high-order conservative schemes solving compressible Euler equations. Zbl 1311.76088Hu, Xiangyu Y.; Adams, Nikolaus A.; Shu, Chi-Wang 63 2013 Optimal error estimates of the semidiscrete local discontinuous Galerkin methods for high order wave equations. Zbl 1247.65121Xu, Yan; Shu, Chi-Wang 62 2012 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. Zbl 1115.65096Xing, Yulong; Shu, Chi-Wang 62 2006 Anti-diffusive flux corrections for high order finite difference WENO schemes. Zbl 1087.76080Xu, Zhengfu; Shu, Chi-Wang 62 2005 Development of nonlinear weighted compact schemes with increasingly higher order accuracy. Zbl 1152.65094Zhang, Shuhai; Jiang, Shufen; Shu, Chi-Wang 61 2008 Numerical experiments on the accuracy of ENO and modified ENO schemes. Zbl 0732.65085Shu, Chi-Wang 61 1990 Locally divergence-free discontinuous Galerkin methods for MHD equations. Zbl 1123.76341Li, Fengyan; Shu, Chi-Wang 60 2005 Positivity preserving semi-Lagrangian discontinuous Galerkin formulation: theoretical analysis and application to the Vlasov-Poisson system. Zbl 1273.65147Qiu, Jing-Mei; Shu, Chi-Wang 58 2011 Stability and error estimates of local discontinuous Galerkin methods with implicit-explicit time-marching for advection-diffusion problems. Zbl 1327.65179Wang, Haijin; Shu, Chi-Wang; Zhang, Qiang 58 2015 The discontinuous Galerkin method with Lax–Wendroff type time discretizations. Zbl 1093.76038Qiu, Jianxian; Dumbser, Michael; Shu, Chi-Wang 55 2005 Inverse Lax-Wendroff procedure for numerical boundary conditions of conservation laws. Zbl 1198.65174Tan, Sirui; Shu, Chi-Wang 55 2010 A high-order discontinuous Galerkin method for 2D incompressible flows. Zbl 0963.76069Liu, Jian-Guo; Shu, Chi-Wang 55 2000 Discontinuous Galerkin methods. Theory, computation and applications. 1st international symposium on DGM, Newport, RI, USA, May 24–26, 1999. Zbl 0935.00043 54 2000 Nonlinearly stable compact schemes for shock calculations. Zbl 0805.65085Cockburn, Bernardo; Shu, Chi-Wang 54 1994 High order WENO and DG methods for time-dependent convection-dominated PDEs: A brief survey of several recent developments. Zbl 1349.65486Shu, Chi-Wang 53 2016 Finite difference WENO schemes with Lax-Wendroff-type time discretizations. Zbl 1034.65073Qiu, Jianxian; Shu, Chi-Wang 53 2003 Local discontinuous Galerkin methods for the Kuramoto-Sivashinsky equations and the Ito-type coupled KdV equations. Zbl 1124.76035Xu, Yan; Shu, Chi-Wang 51 2006 Robust high order discontinuous Galerkin schemes for two-dimensional gaseous detonations. Zbl 1243.80011Wang, Cheng; Zhang, Xiangxiong; Shu, Chi-Wang; Ning, Jianguo 49 2012 An analysis of three different formulations of the discontinuous Galerkin method for diffusion equations. Zbl 1050.65094Zhang, Mengping; Shu, Chi-Wang 49 2003 Local discontinuous Galerkin methods for two classes of two-dimensional nonlinear wave equations. Zbl 1078.35111Xu, Yan; Shu, Chi-Wang 48 2005 Analysis of a local discontinuous Galerkin method for linear time-dependent fourth-order problems. Zbl 1204.65123Dong, Bo; Shu, Chi-Wang 48 2009 Optimal error estimates for discontinuous Galerkin methods based on upwind-biased fluxes for linear hyperbolic equations. Zbl 1332.65148Meng, Xiong; Shu, Chi-Wang; Wu, Boying 48 2016 Conservative high order semi-Lagrangian finite difference WENO methods for advection in incompressible flow. Zbl 1391.76489Qiu, Jing-Mei; Shu, Chi-Wang 48 2011 Maximum-principle-satisfying second order discontinuous Galerkin schemes for convection-diffusion equations on triangular meshes. Zbl 1284.65140Zhang, Yifan; Zhang, Xiangxiong; Shu, Chi-Wang 47 2013 High order conservative Lagrangian schemes with Lax-Wendroff type time discretization for the compressible Euler equations. Zbl 1287.76181Liu, Wei; Cheng, Juan; Shu, Chi-Wang 47 2009 A discontinuous Galerkin finite element method for directly solving the Hamilton-Jacobi equations. Zbl 1124.65090Cheng, Yingda; Shu, Chi-Wang 46 2007 \(L^{2}\) stability analysis of the central discontinuous Galerkin method and a comparison between the central and regular discontinuous Galerkin methods. Zbl 1152.65095Liu, Yingjie; Shu, Chi-Wang; Tadmor, Eitan; Zhang, Mengping 46 2008 A numerical study for the performance of the Runge-Kutta discontinuous Galerkin method based on different numerical fluxes. Zbl 1083.65093Qiu, Jianxian; Khoo, Boo Cheong; Shu, Chi-Wang 46 2006 A WENO-solver for the transients of Boltzmann-Poisson system for semiconductor devices: Performance and comparisons with Monte Carlo methods. Zbl 1034.82063Carrillo, José A.; Gamba, Irene M.; Majorana, Armando; Shu, Chi-Wang 45 2003 An analysis of and a comparison between the discontinuous Galerkin and the spectral finite volume methods. Zbl 1138.76391Zhang, Mengping; Shu, Chi-Wang 44 2005 A survey of high order schemes for the shallow water equations. Zbl 1324.76035Xing, Yulong; Shu, Chi-Wang 42 2014 Stability analysis of inverse Lax-Wendroff boundary treatment of high order compact difference schemes for parabolic equations. Zbl 1481.65145Li, Tingting; Lu, Jianfang; Shu, Chi-Wang 1 2022 An oscillation-free discontinuous Galerkin method for scalar hyperbolic conservation laws. Zbl 1467.65095Lu, Jianfang; Liu, Yong; Shu, Chi-Wang 2 2021 Provably physical-constraint-preserving discontinuous Galerkin methods for multidimensional relativistic MHD equations. Zbl 1480.65271Wu, Kailiang; Shu, Chi-Wang 2 2021 A high order positivity-preserving conservative WENO remapping method on 2D quadrilateral meshes. Zbl 07337779Lei, Nuo; Cheng, Juan; Shu, Chi-Wang 2 2021 A local discontinuous Galerkin method for nonlinear parabolic SPDEs. Zbl 1480.65019Li, Yunzhang; Shu, Chi-Wang; Tang, Shanjian 1 2021 High-order Runge-Kutta discontinuous Galerkin methods with a new type of multi-resolution WENO limiters on tetrahedral meshes. Zbl 1474.65379Zhu, Jun; Shu, Chi-Wang; Qiu, Jianxian 1 2021 A discontinuous Galerkin method and its error estimate for nonlinear fourth-order wave equations. Zbl 1456.65124Tao, Qi; Xu, Yan; Shu, Chi-Wang 1 2021 Enforcing strong stability of explicit Runge-Kutta methods with superviscosity. Zbl 07479324Sun, Zheng; Shu, Chi-Wang 1 2021 A new type of third-order finite volume multi-resolution WENO schemes on tetrahedral meshes. Zbl 1453.65266Zhu, Jun; Shu, Chi-Wang 11 2020 High-order Runge-Kutta discontinuous Galerkin methods with a new type of multi-resolution WENO limiters. Zbl 1453.65351Zhu, Jun; Qiu, Jianxian; Shu, Chi-Wang 10 2020 High-order Runge-Kutta discontinuous Galerkin methods with a new type of multi-resolution WENO limiters on triangular meshes. Zbl 1436.65118Zhu, Jun; Shu, Chi-Wang; Qiu, Jianxian 7 2020 Local discontinuous Galerkin methods with explicit-implicit-null time discretizations for solving nonlinear diffusion problems. Zbl 1434.65196Wang, Haijin; Zhang, Qiang; Wang, Shiping; Shu, Chi-Wang 7 2020 Entropy symmetrization and high-order accurate entropy stable numerical schemes for relativistic MHD equations. Zbl 1450.65089Wu, Kailiang; Shu, Chi-Wang 6 2020 A discontinuous Galerkin method for stochastic conservation laws. Zbl 07149719Li, Yunzhang; Shu, Chi-Wang; Tang, Shanjian 5 2020 Superconvergence analysis of the Runge-Kutta discontinuous Galerkin methods for a linear hyperbolic equation. Zbl 1465.65105Xu, Yuan; Meng, Xiong; Shu, Chi-Wang; Zhang, Qiang 4 2020 On a new WENO algorithm of order \(2 r\) with improved accuracy close to discontinuities. Zbl 07187420Amat, Sergio; Ruiz, Juan; Shu, Chi-Wang 3 2020 Optimal error estimates of the semidiscrete discontinuous Galerkin methods for two dimensional hyperbolic equations on Cartesian meshes using \(P^k\) elements. Zbl 1439.65115Liu, Yong; Shu, Chi-Wang; Zhang, Mengping 3 2020 Well-balanced finite-volume schemes for hydrodynamic equations with general free energy. Zbl 1434.82098Carrillo, José A.; Kalliadasis, Serafim; Perez, Sergio P.; Shu, Chi-Wang 3 2020 On the conservation of finite difference WENO schemes in non-rectangular domains using the inverse Lax-Wendroff boundary treatments. Zbl 1440.65086Ding, Shengrong; Shu, Chi-Wang; Zhang, Mengping 3 2020 An ultraweak-local discontinuous Galerkin method for PDEs with high order spatial derivatives. Zbl 1446.65118Tao, Qi; Xu, Yan; Shu, Chi-Wang 3 2020 Error estimate of the fourth-order Runge-Kutta discontinuous Galerkin methods for linear hyperbolic equations. Zbl 1452.65256Xu, Yuan; Shu, Chi-Wang; Zhang, Qiang 3 2020 Convergence to steady-state solutions of the new type of high-order multi-resolution WENO schemes: a numerical study. Zbl 1476.65200Zhu, Jun; Shu, Chi-Wang 2 2020 An ultra-weak discontinuous Galerkin method with implicit-explicit time-marching for generalized stochastic KdV equations. Zbl 1434.65015Li, Yunzhang; Shu, Chi-Wang; Tang, Shanjian 2 2020 A new WENO-\(2r\) algorithm with progressive order of accuracy close to discontinuities. Zbl 1457.65038Amat, Sergio P.; Ruiz, Juan; Shu, Chi-Wang; Yáñez, Dionisio F. 2 2020 Analysis of optimal superconvergence of an ultraweak-local discontinuous Galerkin method for a time dependent fourth-order equation. Zbl 1476.65242Liu, Yong; Tao, Qi; Shu, Chi-Wang 1 2020 On new strategies to control the accuracy of WENO algorithm close to discontinuities. II: Cell averages and multiresolution. Zbl 1463.65213Amat, Sergio; Ruiz, Juan; Shu, Chiwang 1 2020 Strong stability of explicit Runge-Kutta time discretizations. Zbl 1422.65224Sun, Zheng; Shu, Chi-Wang 12 2019 A new type of multi-resolution WENO schemes with increasingly higher order of accuracy on triangular meshes. Zbl 1452.76143Zhu, Jun; Shu, Chi-Wang 10 2019 Provably positive high-order schemes for ideal magnetohydrodynamics: analysis on general meshes. Zbl 1419.76446Wu, Kailiang; Shu, Chi-Wang 10 2019 Positivity-preserving time discretizations for production-destruction equations with applications to non-equilibrium flows. Zbl 1420.35190Huang, Juntao; Shu, Chi-Wang 9 2019 The \(\mathrm{L}^2\)-norm stability analysis of Runge-Kutta discontinuous Galerkin methods for linear hyperbolic equations. Zbl 1422.65272Xu, Yuan; Zhang, Qiang; Shu, Chi-Wang; Wang, Haijin 7 2019 Implicit-explicit local discontinuous Galerkin methods with generalized alternating numerical fluxes for convection-diffusion problems. Zbl 1434.65195Wang, Haijin; Zhang, Qiang; Shu, Chi-Wang 6 2019 An energy-conserving ultra-weak discontinuous Galerkin method for the generalized Korteweg-de Vries equation. Zbl 1407.65187Fu, Guosheng; Shu, Chi-Wang 6 2019 A third-order unconditionally positivity-preserving scheme for production-destruction equations with applications to non-equilibrium flows. Zbl 1444.35125Huang, Juntao; Zhao, Weifeng; Shu, Chi-Wang 6 2019 Stability analysis and error estimates of arbitrary Lagrangian-Eulerian discontinuous Galerkin method coupled with Runge-Kutta time-marching for linear conservation laws. Zbl 1418.65141Zhou, Lingling; Xia, Yinhua; Shu, Chi-Wang 6 2019 An entropy stable high-order discontinuous Galerkin method for cross-diffusion gradient flow systems. Zbl 1420.65095Sun, Zheng; Carrillo, José A.; Shu, Chi-Wang 6 2019 Superconvergence of energy-conserving discontinuous Galerkin methods for linear hyperbolic equations. Zbl 1449.65250Liu, Yong; Shu, Chi-Wang; Zhang, Mengping 5 2019 Local discontinuous Galerkin methods with implicit-explicit time-marching for time-dependent incompressible fluid flow. Zbl 1405.65129Wang, Haijin; Liu, Yunxian; Zhang, Qiang; Shu, Chi-Wang 5 2019 High order finite difference Hermite WENO schemes for the Hamilton-Jacobi equations on unstructured meshes. Zbl 1411.76111Zheng, Feng; Shu, Chi-Wang; Qiu, Jianxian 4 2019 On new strategies to control the accuracy of WENO algorithms close to discontinuities. Zbl 1436.65095Amat, Sergio; Ruiz, Juan; Shu, Chi-Wang 4 2019 Numerical solutions of stochastic PDEs driven by arbitrary type of noise. Zbl 1475.60112Chen, Tianheng; Rozovskii, Boris; Shu, Chi-Wang 3 2019 Preface to the focused issue on fractional derivatives and general nonlocal models. Zbl 1449.00002 1 2019 Certified offline-free reduced basis (COFRB) methods for stochastic differential equations driven by arbitrary types of noise. Zbl 1440.65250Liu, Yong; Chen, Tianheng; Chen, Yanlai; Shu, Chi-Wang 1 2019 High order arbitrary Lagrangian-Eulerian finite difference WENO scheme for Hamilton-Jacobi equations. Zbl 1473.65114Li, Yue; Cheng, Juan; Xia, Yinhua; Shu, Chi-Wang 1 2019 Optimal energy-conserving discontinuous Galerkin methods for linear symmetric hyperbolic systems. Zbl 1452.65230Fu, Guosheng; Shu, Chi-Wang 1 2019 Bounded and compact weighted essentially nonoscillatory limiters for discontinuous Galerkin schemes: triangular elements. Zbl 1452.76097Mazaheri, Alireza; Shu, Chi-Wang; Perrier, Vincent 1 2019 Assessment of aeroacoustic resolution properties of DG schemes and comparison with DRP schemes. Zbl 1453.76064Cheng, Ziqiang; Fang, Jinwei; Shu, Chi-Wang; Zhang, Mengping 1 2019 A new type of multi-resolution WENO schemes with increasingly higher order of accuracy. Zbl 1416.65286Zhu, Jun; Shu, Chi-Wang 33 2018 A discontinuous Galerkin method for nonlinear parabolic equations and gradient flow problems with interaction potentials. Zbl 1380.65287Sun, Zheng; Carrillo, José A.; Shu, Chi-Wang 18 2018 Superconvergence of discontinuous Galerkin method for scalar nonlinear hyperbolic equations. Zbl 1450.65116Cao, Waixiang; Shu, Chi-Wang; Yang, Yang; Zhang, Zhimin 18 2018 Entropy stable high order discontinuous Galerkin methods for ideal compressible MHD on structured meshes. Zbl 1380.76162Liu, Yong; Shu, Chi-Wang; Zhang, Mengping 15 2018 Bound-preserving modified exponential Runge-Kutta discontinuous Galerkin methods for scalar hyperbolic equations with stiff source terms. Zbl 1422.65259Huang, Juntao; Shu, Chi-Wang 11 2018 A provably positive discontinuous Galerkin method for multidimensional ideal magnetohydrodynamics. Zbl 1404.65184Wu, Kailiang; Shu, Chi-Wang 10 2018 Implicit positivity-preserving high-order discontinuous Galerkin methods for conservation laws. Zbl 1380.65285Qin, Tong; Shu, Chi-Wang 9 2018 Third order implicit-explicit Runge-Kutta local discontinuous Galerkin methods with suitable boundary treatment for convection-diffusion problems with Dirichlet boundary conditions. Zbl 1448.65178Wang, Haijin; Zhang, Qiang; Shu, Chi-Wang 8 2018 On local conservation of numerical methods for conservation laws. Zbl 1410.65327Shi, Cengke; Shu, Chi-Wang 7 2018 Discontinuous Galerkin methods for Maxwell’s equations in Drude metamaterials on unstructured meshes. Zbl 1462.65156Shi, Cengke; Li, Jichun; Shu, Chi-Wang 7 2018 Optimal error estimates of the semidiscrete central discontinuous Galerkin methods for linear hyperbolic equations. Zbl 1383.65108Liu, Yong; Shu, Chi-Wang; Zhang, Mengping 6 2018 Bound-preserving high-order schemes for hyperbolic equations: survey and recent developments. Zbl 1412.65155Shu, Chi-Wang 5 2018 Conservative high order positivity-preserving discontinuous Galerkin methods for linear hyperbolic and radiative transfer equations. Zbl 1407.65196Ling, Dan; Cheng, Juan; Shu, Chi-Wang 5 2018 Positivity-preserving high-order schemes for conservation laws on arbitrarily distributed point clouds with a simple WENO limiter. Zbl 1414.65012Du, Jie; Shu, Chi-Wang 3 2018 Discontinuous Galerkin methods for a kinetic model of self-organized dynamics. Zbl 1404.65168Filbet, Francis; Shu, Chi-Wang 1 2018 Entropy stable high order discontinuous Galerkin methods with suitable quadrature rules for hyperbolic conservation laws. Zbl 1380.65253Chen, Tianheng; Shu, Chi-Wang 72 2017 Optimal non-dissipative discontinuous Galerkin methods for Maxwell’s equations in Drude metamaterials. Zbl 1370.74143Li, Jichun; Shi, Cengke; Shu, Chi-Wang 28 2017 Local discontinuous Galerkin method for the Keller-Segel chemotaxis model. Zbl 1384.92015Li, Xingjie Helen; Shu, Chi-Wang; Yang, Yang 27 2017 A new troubled-cell indicator for discontinuous Galerkin methods for hyperbolic conservation laws. Zbl 1380.65262Fu, Guosheng; Shu, Chi-Wang 18 2017 H(div) conforming and DG methods for incompressible Euler’s equations. Zbl 1433.76085Guzmán, Johnny; Shu, Chi-Wang; Sequeira, Filánder A. 16 2017 Stability of the fourth order Runge-Kutta method for time-dependent partial differential equations. Zbl 1381.65079Sun, Zheng; Shu, Chi-Wang 15 2017 Unconditional energy stability analysis of a second order implicit-explicit local discontinuous Galerkin method for the Cahn-Hilliard equation. Zbl 1383.65105Song, Huailing; Shu, Chi-Wang 15 2017 Superconvergence of discontinuous Galerkin methods for 1-D linear hyperbolic equations with degenerate variable coefficients. Zbl 1382.65274Cao, Waixiang; Shu, Chi-Wang; Zhang, Zhimin 14 2017 Numerical study on the convergence to steady state solutions of a new class of high order WENO schemes. Zbl 1380.76074Zhu, Jun; Shu, Chi-Wang 12 2017 A second-order asymptotic-preserving and positivity-preserving discontinuous Galerkin scheme for the Kerr-Debye model. Zbl 1360.65235Huang, Juntao; Shu, Chi-Wang 9 2017 Finite difference Hermite WENO schemes for the Hamilton-Jacobi equations. Zbl 1415.65204Zheng, Feng; Shu, Chi-Wang; Qiu, Jianxian 9 2017 Error estimates to smooth solutions of semi-discrete discontinuous Galerkin methods with quadrature rules for scalar conservation laws. Zbl 1361.65067Huang, Juntao; Shu, Chi-Wang 8 2017 Maximum-principle-satisfying space-time conservation element and solution element scheme applied to compressible multifluids. Zbl 1378.76086Shen, Hua; Wen, Chih-Yung; Parsani, Matteo; Shu, Chi-Wang 8 2017 Stability analysis of the inverse Lax-Wendroff boundary treatment for high order central difference schemes for diffusion equations. Zbl 1361.65062Li, Tingting; Shu, Chi-Wang; Zhang, Mengping 5 2017 Stability analysis and error estimates of Lax-Wendroff discontinuous Galerkin methods for linear conservation laws. Zbl 1373.65063Sun, Zheng; Shu, Chi-Wang 5 2017 Runge-Kutta discontinuous Galerkin method with a simple and compact Hermite WENO limiter on unstructured meshes. Zbl 07413964Zhu, Jun; Zhong, Xinghui; Shu, Chi-Wang; Qiu, Jianxian 4 2017 Analysis of an embedded discontinuous Galerkin method with implicit-explicit time-marching for convection-diffusion problems. Zbl 1380.65261Fu, Guosheng; Shu, Chi-Wang 4 2017 Stability analysis and error estimates of local discontinuous Galerkin methods with implicit-explicit time-marching for the time-dependent fourth order PDEs. Zbl 1407.65204Wang, Haijin; Zhang, Qiang; Shu, Chi-Wang 4 2017 Positivity-preserving and symmetry-preserving Lagrangian schemes for compressible Euler equations in cylindrical coordinates. Zbl 1390.76473Ling, Dan; Cheng, Juan; Shu, Chi-Wang 3 2017 Handbook on numerical methods for hyperbolic problems. Applied and modern issues. Zbl 1364.65001 2 2017 A phase-based interior penalty discontinuous Galerkin method for the Helmholtz equation with spatially varying wavenumber. Zbl 1439.65183Lam, Chi Yeung; Shu, Chi-Wang 2 2017 Bound-preserving high order finite volume schemes for conservation laws and convection-diffusion equations. Zbl 1372.65251Shu, Chi-Wang 2 2017 A simple bound-preserving sweeping technique for conservative numerical approximations. Zbl 1381.65087Liu, Yuan; Cheng, Yingda; Shu, Chi-Wang 2 2017 A brief survey on high order numerical methods for convection dominated problems. Zbl 1380.65182Shu, Chi-Wang 1 2017 Inverse Lax-Wendroff procedure for numerical boundary treatment of hyperbolic equations. Zbl 1366.65080Shu, C.-W.; Tan, S. 1 2017 An efficient class of WENO schemes with adaptive order. Zbl 1422.65146Balsara, Dinshaw S.; Garain, Sudip; Shu, Chi-Wang 81 2016 High order WENO and DG methods for time-dependent convection-dominated PDEs: A brief survey of several recent developments. Zbl 1349.65486Shu, Chi-Wang 53 2016 Optimal error estimates for discontinuous Galerkin methods based on upwind-biased fluxes for linear hyperbolic equations. Zbl 1332.65148Meng, Xiong; Shu, Chi-Wang; Wu, Boying 48 2016 Bound-preserving discontinuous Galerkin methods for relativistic hydrodynamics. Zbl 1349.83037Qin, Tong; Shu, Chi-Wang; Yang, Yang 26 2016 Local discontinuous Galerkin methods with implicit-explicit time-marching for multi-dimensional convection-diffusion problems. Zbl 1351.65078Wang, Haijin; Wang, Shiping; Zhang, Qiang; Shu, Chi-Wang 25 2016 Runge-Kutta discontinuous Galerkin method with a simple and compact Hermite WENO limiter. Zbl 1373.76113Zhu, Jun; Zhong, Xinghui; Shu, Chi-Wang; Qiu, Jianxian 23 2016 Stability analysis and error estimates of local discontinuous Galerkin methods with implicit-explicit time-marching for nonlinear convection-diffusion problems. Zbl 1410.65383Wang, Haijin; Shu, Chi-Wang; Zhang, Qiang 21 2016 Positivity-preserving cell-centered Lagrangian schemes for multi-material compressible flows: from first-order to high-orders. II: The two-dimensional case. Zbl 1351.76128Vilar, François; Shu, Chi-Wang; Maire, Pierre-Henri 20 2016 Positivity-preserving cell-centered Lagrangian schemes for multi-material compressible flows: from first-order to high-orders. I: The one-dimensional case. Zbl 1351.76127Vilar, François; Shu, Chi-Wang; Maire, Pierre-Henri 17 2016 Inverse Lax-Wendroff procedure for numerical boundary conditions of convection-diffusion equations. Zbl 1349.65319Lu, Jianfang; Fang, Jinwei; Tan, Sirui; Shu, Chi-Wang; Zhang, Mengping 14 2016 Analysis of the local discontinuous Galerkin method for the drift-diffusion model of semiconductor devices. Zbl 1342.65183Liu, YunXian; Shu, Chi-Wang 11 2016 High order fixed-point sweeping WENO methods for steady state of hyperbolic conservation laws and its convergence study. Zbl 1388.65068Wu, Liang; Zhang, Yong-Tao; Zhang, Shuhai; Shu, Chi-Wang 9 2016 Stability analysis of the inverse Lax-Wendroff boundary treatment for high order upwind-biased finite difference schemes. Zbl 1333.65101Li, Tingting; Shu, Chi-Wang; Zhang, Mengping 9 2016 ...and 281 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 7,961 Authors 254 Shu, Chi-Wang 94 Dumbser, Michael 81 Qiu, Jianxian 51 Kurganov, Alexander 50 Cockburn, Bernardo 50 Xu, Yan 46 Osher, Stanley Joel 45 Adams, Nikolaus A. 43 Baccouch, Mahboub 43 Zhu, Jun 42 Qiu, Jingmei 42 Xu, Kun 41 Dawson, Clint N. 41 Liu, Hailiang 40 Cheng, Yingda 40 Li, Jichun 38 Toro, Eleuterio F. 37 Abgrall, Rémi 37 Xing, Yulong 37 Zhang, Mengping 36 Balsara, Dinshaw S. 36 Don, Wai Sun 36 Hesthaven, Jan S. 35 Liu, Tiegang 35 Xiao, Feng 34 Bürger, Raimund 34 Li, Fengyan 34 Mulet, Pep 33 Dehghan Takht Fooladi, Mehdi 32 Yang, Yang 31 Gassner, Gregor J. 30 Christlieb, Andrew J. 30 Yu, Xijun 29 Deng, Xiaogang 29 Fedkiw, Ronald P. 29 Gao, Zhen 29 Huang, Yunqing 29 Qian, Jianliang 29 Tang, Huazhong 28 Kuzmin, Dmitri 28 Munz, Claus-Dieter 27 Chertock, Alina E. 27 Ren, Yuxin 27 Xia, Yinhua 26 Castro, Manuel J. 26 Loubère, Raphaël 26 Ryan, Jennifer K. 26 Zhang, Yongtao 25 Amat, Sergio P. 25 Boscheri, Walter 25 Jameson, Antony 25 Zhang, Zhimin 24 Guermond, Jean-Luc 24 Luo, Hong 24 van der Vegt, Jaap J. 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