Edit Profile Shu, Chi-Wang Compute Distance To: Compute Author ID: shu.chi-wang Published as: Shu, C.; Shu, C.-W.; Shu, Chi-Wang; Shu, Chi-wang; Shu, Chiwang Homepage: http://www.dam.brown.edu/people/shu/ External Links: MGP · Wikidata · ResearchGate · dblp · GND Documents Indexed: 415 Publications since 1987, including 10 Books Biographic References: 1 Publication all top 5 Co-Authors 25 single-authored 38 Zhang, Mengping 18 Xu, Yan 18 Zhang, Qiang 16 Cockburn, Bernardo 16 Qiu, Jianxian 15 Cheng, Juan 13 Gottlieb, David I. 13 Zhang, Yongtao 12 Xing, Yulong 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 Zhu, Jun 8 Liu, Yingjie 8 Xia, Yinhua 7 E, Weinan 6 Gottlieb, Sigal 6 Jerome, Joseph W. 6 Li, Fengyan 6 Majorana, Armando 6 Osher, Stanley Joel 6 Tadmor, Eitan 5 Hu, Changqing 5 Huang, Juntao 5 Liu, Yunxian 5 Qiu, Jingmei 5 Sun, Zheng 5 Tan, Sirui 5 Xu, Zhiliang 5 Yee, Helen C. 4 Amat, Sergio P. 4 Chou, Ching-Shan 4 Du, Jie 4 Fu, Guosheng 4 Meng, Xiong 4 Ruiz, Juan P. 4 Sjogreen, Bjorn 4 Xiong, Tao 4 Xu, Zhengfu 3 Abgrall, Rémi 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 Hesthaven, Jan S. 3 Jiang, Shufen 3 Jiang, Yan 3 Karniadakis, George Em 3 Ling, Dan 3 Noelle, Sebastian 3 Ryan, Jennifer K. 3 Shi, Cengke 3 Vilar, François 3 Wu, Boying 3 Wu, Kailiang 3 Yan, Jue 3 Yang, Yang 3 Zhang, Hanxin 3 Zhang, Zhimin 3 Zhong, Xinghui 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 Cheng, Shiu-Yuen 2 Dumbser, Michael 2 Erlebacher, Gordon 2 Fang, Jinwei 2 Jiang, Guangshan 2 Ketcheson, David I. 2 Kotov, Dmitry V. 2 Lam, William H. K. 2 Lepsky, Olga 2 Levy, Doron 2 Li, Jichun 2 Li, Tingting 2 Li, Yunzhang 2 Liu, Jianguo 2 Liu, Wei 2 Liu, Xuliang 2 Liu, Yuan 2 Liu, Yuanyuan 2 Lu, Jianfang 2 Luskin, Mitchell 2 Maire, Pierre-Henri 2 Ning, Jianguo 2 Qin, Tong 2 Sapiro, Guillermo ...and 155 more Co-Authors all top 5 Serials 96 Journal of Computational Physics 42 Journal of Scientific Computing 28 SIAM Journal on Numerical Analysis 23 SIAM Journal on Scientific Computing 16 Communications in Computational Physics 14 Mathematics of Computation 11 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 10 Computer Methods in Applied Mechanics and Engineering 8 Computers and Fluids 8 Journal of Computational and Applied Mathematics 7 Numerische Mathematik 7 Journal of Computational Mathematics 7 Applied Numerical Mathematics 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 4 International Journal of Numerical Analysis and Modeling 3 SIAM Review 3 Multiscale Modeling & Simulation 3 Communications on Applied Mathematics and Computation 2 Computers & Mathematics with Applications 2 IMA Journal of Numerical Analysis 2 Journal of Fluid Mechanics 2 Transport Theory and Statistical Physics 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 Handbook of Numerical Analysis 2 Kinetic and Related Models 1 AIAA Journal 1 International Journal for Numerical Methods in Fluids 1 Nonlinearity 1 Physics of Fluids, A 1 Applied Mathematics and Computation 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 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 Contemporary Mathematics 1 Lecture Notes in Mathematics 1 Lecture Notes in Computational Science and Engineering 1 Acta Mechanica Sinica 1 Inverse Problems and Imaging 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 Annals of Mathematical Sciences and Applications 1 Advanced Courses in Mathematics – CRM Barcelona all top 5 Fields 324 Numerical analysis (65-XX) 208 Partial differential equations (35-XX) 140 Fluid mechanics (76-XX) 27 Statistical mechanics, structure of matter (82-XX) 10 General and overarching topics; collections (00-XX) 9 Harmonic analysis on Euclidean spaces (42-XX) 9 Biology and other natural sciences (92-XX) 8 Calculus of variations and optimal control; optimization (49-XX) 8 Mechanics of deformable solids (74-XX) 7 Operations research, mathematical programming (90-XX) 6 Optics, electromagnetic theory (78-XX) 6 Classical thermodynamics, heat transfer (80-XX) 5 History and biography (01-XX) 5 Special functions (33-XX) 5 Ordinary differential equations (34-XX) 4 Probability theory and stochastic processes (60-XX) 4 Astronomy and astrophysics (85-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Computer science (68-XX) 3 Mechanics of particles and systems (70-XX) 2 Approximations and expansions (41-XX) 2 Integral equations (45-XX) 1 Combinatorics (05-XX) 1 Nonassociative rings and algebras (17-XX) 1 Group theory and generalizations (20-XX) 1 Topological groups, Lie groups (22-XX) 1 Real functions (26-XX) 1 Differential geometry (53-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 352 Publications have been cited 18,812 times in 6,146 Documents Cited by ▼ Year ▼ Efficient implementation of weighted ENO schemes. Zbl 0877.65065Jiang, Guang-Shan; Shu, Chi-Wang 1,363 1996 Efficient implementation of essentially nonoscillatory shock-capturing schemes. Zbl 0653.65072Shu, Chi-Wang; Osher, Stanley 1,319 1988 Efficient implementation of essentially nonoscillatory shock-capturing schemes. II. Zbl 0674.65061Shu, Chi-Wang; Osher, Stanley 760 1989 The local discontinuous Galerkin method for time-dependent convection-diffusion systems. Zbl 0927.65118Cockburn, Bernardo; Shu, Chi-Wang 756 1998 TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. II: General framework. Zbl 0662.65083Cockburn, Bernardo; Shu, Chi-Wang 679 1989 The Runge-Kutta discontinuous Galerkin method for conservation laws. I: Multidimensional systems. Zbl 0920.65059Cockburn, Bernardo; Shu, Chi-Wang 649 1998 Strong stability-preserving high-order time discretization methods. Zbl 0967.65098Gottlieb, Sigal; Shu, Chi-Wang; Tadmor, Eitan 603 2001 Runge–Kutta discontinuous Galerkin methods for convection-dominated problems. Zbl 1065.76135Cockburn, Bernardo; Shu, Chi-Wang 580 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 483 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 477 1990 Total variation diminishing Runge-Kutta schemes. Zbl 0897.65058Gottlieb, Sigal; Shu, Chi-Wang 443 1998 Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws. Zbl 0927.65111Shu, Chi-Wang 389 1998 Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy. Zbl 0961.65078Balsara, Dinshaw S.; Shu, Chi-Wang 340 2000 Total-variation-diminishing time discretizations. Zbl 0662.65081Shu, Chiwang 303 1988 The development of discontinuous Galerkin methods. Zbl 0989.76045Cockburn, Bernardo; Karniadakis, George E.; Shu, Chi-Wang 280 2000 Weighted essentially non-oscillatory schemes on triangular meshes. Zbl 0926.65090Hu, Changqing; Shu, Chi-Wang 259 1999 High order weighted essentially nonoscillatory schemes for convection dominated problems. Zbl 1160.65330Shu, Chi-Wang 251 2009 High-order essentially nonoscillatory schemes for Hamilton-Jacobi equations. Zbl 0736.65066Osher, Stanley; Shu, Chi-Wang 229 1991 The Runge-Kutta local projection \(P^ 1\)-discontinuous-Galerkin finite element method for scalar conservation laws. Zbl 0732.65094Cockburn, Bernardo; Shu, Chi-Wang 193 1991 On the Gibbs phenomenon and its resolution. Zbl 0885.42003Gottlieb, David; Shu, Chi-Wang 191 1997 On maximum-principle-satisfying high order schemes for scalar conservation laws. Zbl 1187.65096Zhang, Xiangxiong; Shu, Chi-Wang 173 2010 On positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations on rectangular meshes. Zbl 1282.76128Zhang, Xiangxiong; Shu, Chi-Wang 168 2010 A technique of treating negative weights in WENO schemes. Zbl 0992.65094Shi, Jing; Hu, Changqing; Shu, Chi-Wang 146 2002 A local discontinuous Galerkin method for KdV type equations. Zbl 1021.65050Yan, Jue; Shu, Chi-Wang 142 2002 Runge-Kutta discontinuous Galerkin method using WENO limiters. Zbl 1077.65109Qiu, Jianxian; Shu, Chi-Wang 132 2005 Hermite WENO schemes and their application as limiters for Runge-Kutta discontinuous Galerkin method: One-dimensional case. Zbl 1039.65068Qiu, Jianxian; Shu, Chi-Wang 129 2004 TVB uniformly high-order schemes for conservation laws. Zbl 0628.65075Shu, Chiwang 125 1987 High order finite difference WENO schemes with the exact conservation property for the shallow water equations. Zbl 1114.76340Xing, Yulong; Shu, Chi-Wang 113 2005 Strong stability preserving Runge-Kutta and multistep time discretizations. Zbl 1241.65064Gottlieb, Sigal; Ketcheson, David; Shu, Chi-Wang 112 2011 Maximum-principle-satisfying and positivity-preserving high-order schemes for conservation laws: survey and new developments. Zbl 1222.65107Zhang, Xiangxiong; Shu, Chi-Wang 102 2011 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 98 2005 High order strong stability preserving time discretizations. Zbl 1203.65135Gottlieb, Sigal; Ketcheson, David I.; Shu, Chi-Wang 97 2009 Locally divergence-free discontinuous Galerkin methods for the Maxwell equations. Zbl 1049.78019Cockburn, Bernardo; Li, Fengyan; Shu, Chi-Wang 97 2004 Local discontinuous Galerkin methods for high-order time-dependent partial differential equations. Zbl 1364.65205Xu, Yan; Shu, Chi-Wang 95 2010 On the construction, comparison, and local characteristic decomposition for high-order central WENO schemes. Zbl 1018.65106Qiu, Jianxian; Shu, Chi-Wang 94 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 88 2007 Local discontinuous Galerkin methods for nonlinear Schrödinger equations. Zbl 1072.65130Xu, Yan; Shu, Chi-Wang 86 2005 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 82 2006 Error estimates to smooth solutions of Runge-Kutta discontinuous Galerkin methods for scalar conservation laws. Zbl 1078.65080Zhang, Qiang; Shu, Chi-Wang 81 2004 High-order finite difference and finite volume WENO schemes and discontinuous Galerkin methods for CFD. Zbl 1034.76044Shu, Chi-Wang 81 2003 Runge-Kutta discontinuous Galerkin method using WENO limiters II: Unstructured meshes. Zbl 1157.65453Zhu, Jun; Qiu, Jianxian; Shu, Chi-Wang; Dumbser, Michael 80 2008 Resolution of high order WENO schemes for complicated flow structures. Zbl 1047.76081Shi, Jing; Zhang, Yong-Tao; Shu, Chi-Wang 80 2003 A discontinuous Galerkin finite element method for Hamilton-Jacobi equations. Zbl 0946.65090Hu, Changqing; Shu, Chi-Wang 78 1999 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 74 2012 Discontinuous Galerkin methods. Theory, computation and applications. 1st international symposium on DGM, Newport, RI, USA, May 24–26, 1999. Zbl 0935.00043Cockburn, Bernardo (ed.); Karniadakis, George E. (ed.); Shu, Chi-Wang (ed.) 74 2000 High-order WENO schemes for Hamilton-Jacobi equations on triangular meshes. Zbl 1034.65051Zhang, Yong-Tao; Shu, Chi-Wang 72 2003 A comparison of troubled-cell indicators for Runge-Kutta discontinuous Galerkin methods using weighted essentially nonoscillatory limiters. Zbl 1092.65084Qiu, Jianxian; Shu, Chi-Wang 71 2005 Local discontinuous Galerkin methods for partial differential equations with higher order derivatives. Zbl 1003.65115Yan, Jue; Shu, Chi-Wang 70 2002 On a cell entropy inequality for discontinuous Galerkin methods. Zbl 0801.65098Jiang, Guangshan; Shu, Chi-Wang 70 1994 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 70 1992 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 69 2010 Positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations with source terms. Zbl 1391.76375Zhang, Xiangxiong; Shu, Chi-Wang 67 2011 A high-order ENO conservative Lagrangian type scheme for the compressible Euler equations. Zbl 1126.76035Cheng, Juan; Shu, Chi-Wang 66 2007 Third order WENO scheme on three dimensional tetrahedral meshes. Zbl 1364.65177Zhang, Yong-Tao; Shu, Chi-Wang 64 2009 A discontinuous Galerkin finite element method for time dependent partial differential equations with higher order derivatives. Zbl 1141.65075Cheng, Yingda; Shu, Chi-Wang 63 2008 Local discontinuous Galerkin methods for the Cahn-Hilliard type equations. Zbl 1131.65088Xia, Yinhua; Xu, Yan; Shu, Chi-Wang 63 2007 Local discontinuous Galerkin methods for nonlinear dispersive equations. Zbl 1055.65109Levy, Doron; Shu, Chi-Wang; Yan, Jue 62 2004 Enhanced accuracy by post-processing for finite element methods for hyperbolic equations. Zbl 1015.65049Cockburn, Bernardo; Luskin, Mitchell; Shu, Chi-Wang; Süli, Endre 62 2003 On positivity preserving finite volume schemes for Euler equations. Zbl 0857.76062Perthame, Benoit; Shu, Chi-Wang 61 1996 Small-scale structures in Boussinesq convection. Zbl 0822.76087E, Weinan; Shu, Chi-Wang 61 1994 Numerical experiments on the accuracy of ENO and modified ENO schemes. Zbl 0732.65085Shu, Chi-Wang 61 1990 A local discontinuous Galerkin method for the Camassa-Holm equation. Zbl 1173.65063Xu, Yan; Shu, Chi-Wang 60 2008 High order ENO and WENO schemes for computational fluid dynamics. Zbl 0937.76044Shu, Chi-Wang 59 1999 Central discontinuous Galerkin methods on overlapping cells with a nonoscillatory hierarchical reconstruction. Zbl 1157.65450Liu, Yingjie; Shu, Chi-Wang; Tadmor, Eitan; Zhang, Mengping 58 2007 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 56 2013 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 56 2010 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 56 2006 Positivity-preserving high order finite difference WENO schemes for compressible Euler equations. Zbl 1426.76493Zhang, Xiangxiong; Shu, Chi-Wang 55 2012 Locally divergence-free discontinuous Galerkin methods for MHD equations. Zbl 1123.76341Li, Fengyan; Shu, Chi-Wang 52 2005 The discontinuous Galerkin method with Lax–Wendroff type time discretizations. Zbl 1093.76038Qiu, Jianxian; Dumbser, Michael; Shu, Chi-Wang 50 2005 Finite difference WENO schemes with Lax-Wendroff-type time discretizations. Zbl 1034.65073Qiu, Jianxian; Shu, Chi-Wang 50 2003 Nonlinearly stable compact schemes for shock calculations. Zbl 0805.65085Cockburn, Bernardo; Shu, Chi-Wang 50 1994 An efficient class of WENO schemes with adaptive order. Zbl 1422.65146Balsara, Dinshaw S.; Garain, Sudip; Shu, Chi-Wang 48 2016 Anti-diffusive flux corrections for high order finite difference WENO schemes. Zbl 1087.76080Xu, Zhengfu; Shu, Chi-Wang 48 2005 Analysis of optimal superconvergence of discontinuous Galerkin method for linear hyperbolic equations. Zbl 1276.65055Yang, Yang; Shu, Chi-Wang 47 2012 Positivity preserving semi-Lagrangian discontinuous Galerkin formulation: theoretical analysis and application to the Vlasov-Poisson system. Zbl 1273.65147Qiu, Jing-Mei; Shu, Chi-Wang 47 2011 Error estimates of the semi-discrete local discontinuous Galerkin method for nonlinear convection-diffusion and KdV equations. Zbl 1173.65338Xu, Yan; Shu, Chi-Wang 47 2007 Positivity-preserving method for high-order conservative schemes solving compressible Euler equations. Zbl 1311.76088Hu, Xiangyu Y.; Adams, Nikolaus A.; Shu, Chi-Wang 45 2013 Development of nonlinear weighted compact schemes with increasingly higher order accuracy. Zbl 1152.65094Zhang, Shuhai; Jiang, Shufen; Shu, Chi-Wang 45 2008 A high-order discontinuous Galerkin method for 2D incompressible flows. Zbl 0963.76069Liu, Jian-Guo; Shu, Chi-Wang 45 2000 Inverse Lax-Wendroff procedure for numerical boundary conditions of conservation laws. Zbl 1198.65174Tan, Sirui; Shu, Chi-Wang 44 2010 Local discontinuous Galerkin methods for the Kuramoto-Sivashinsky equations and the Ito-type coupled KdV equations. Zbl 1124.76035Xu, Yan; Shu, Chi-Wang 44 2006 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 42 2015 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 42 2009 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 42 2003 Optimal error estimates of the semidiscrete local discontinuous Galerkin methods for high order wave equations. Zbl 1247.65121Xu, Yan; Shu, Chi-Wang 41 2012 An analysis of and a comparison between the discontinuous Galerkin and the spectral finite volume methods. Zbl 1138.76391Zhang, Mengping; Shu, Chi-Wang 41 2005 An analysis of three different formulations of the discontinuous Galerkin method for diffusion equations. Zbl 1050.65094Zhang, Mengping; Shu, Chi-Wang 41 2003 \(L^{2}\) 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 40 2008 A discontinuous Galerkin finite element method for directly solving the Hamilton-Jacobi equations. Zbl 1124.65090Cheng, Yingda; Shu, Chi-Wang 39 2007 Robust high order discontinuous Galerkin schemes for two-dimensional gaseous detonations. Zbl 1243.80011Wang, Cheng; Zhang, Xiangxiong; Shu, Chi-Wang; Ning, Jianguo 38 2012 Conservative high order semi-Lagrangian finite difference WENO methods for advection in incompressible flow. Zbl 1391.76489Qiu, Jing-Mei; Shu, Chi-Wang 37 2011 Analysis of a local discontinuous Galerkin method for linear time-dependent fourth-order problems. Zbl 1204.65123Dong, Bo; Shu, Chi-Wang 37 2009 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 37 2006 Local discontinuous Galerkin methods for two classes of two-dimensional nonlinear wave equations. Zbl 1078.35111Xu, Yan; Shu, Chi-Wang 37 2005 Maximum-principle-satisfying second order discontinuous Galerkin schemes for convection-diffusion equations on triangular meshes. Zbl 1284.65140Zhang, Yifan; Zhang, Xiangxiong; Shu, Chi-Wang 36 2013 A survey of high order schemes for the shallow water equations. Zbl 1324.76035Xing, Yulong; Shu, Chi-Wang 33 2014 Superconvergence of discontinuous Galerkin methods for scalar nonlinear conservation laws in one space dimension. Zbl 1267.65115Meng, Xiong; Shu, Chi-Wang; Zhang, Qiang; Wu, Boying 33 2012 On the advantage of well-balanced schemes for moving-water equilibria of the shallow water equations. Zbl 1409.76086Xing, Yulong; Shu, Chi-Wang; Noelle, Sebastian 33 2011 Efficient time discretization for local discontinuous Galerkin methods. Zbl 1141.65076Xia, Yinhua; Xu, Yan; Shu, Chi-Wang 33 2007 An ultraweak-local discontinuous Galerkin method for PDEs with high order spatial derivatives. Zbl 1446.65118Tao, Qi; Xu, Yan; Shu, Chi-Wang 1 2020 On a new WENO algorithm of order \(2 r\) with improved accuracy close to discontinuities. Zbl 07187420Amat, Sergio; Ruiz, Juan; Shu, Chi-Wang 1 2020 A discontinuous Galerkin method for stochastic conservation laws. Zbl 07149719Li, Yunzhang; Shu, Chi-Wang; Tang, Shanjian 1 2020 Strong stability of explicit Runge-Kutta time discretizations. Zbl 1422.65224Sun, Zheng; Shu, Chi-Wang 6 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 3 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 3 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 3 2019 Provably positive high-order schemes for ideal magnetohydrodynamics: analysis on general meshes. Zbl 1419.76446Wu, Kailiang; Shu, Chi-Wang 3 2019 Positivity-preserving time discretizations for production-destruction equations with applications to non-equilibrium flows. Zbl 1420.35190Huang, Juntao; Shu, Chi-Wang 3 2019 An energy-conserving ultra-weak discontinuous Galerkin method for the generalized Korteweg-de Vries equation. Zbl 1407.65187Fu, Guosheng; Shu, Chi-Wang 3 2019 On new strategies to control the accuracy of WENO algorithms close to discontinuities. Zbl 1436.65095Amat, Sergio; Ruiz, Juan; Shu, Chi-Wang 2 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 2 2019 Superconvergence of energy-conserving discontinuous Galerkin methods for linear hyperbolic equations. Zbl 1449.65250Liu, Yong; Shu, Chi-Wang; Zhang, Mengping 1 2019 Numerical solutions of stochastic PDEs driven by arbitrary type of noise. Zbl 07114866Chen, Tianheng; Rozovskii, Boris; Shu, Chi-Wang 1 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 1 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 1 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 1 2019 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 12 2018 Superconvergence of discontinuous Galerkin method for scalar nonlinear hyperbolic equations. Zbl 1450.65116Cao, Waixiang; Shu, Chi-Wang; Yang, Yang; Zhang, Zhimin 10 2018 A new type of multi-resolution WENO schemes with increasingly higher order of accuracy. Zbl 1416.65286Zhu, Jun; Shu, Chi-Wang 7 2018 Entropy stable high order discontinuous Galerkin methods for ideal compressible MHD on structured meshes. Zbl 1380.76162Liu, Yong; Shu, Chi-Wang; Zhang, Mengping 7 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 6 2018 A provably positive discontinuous Galerkin method for multidimensional ideal magnetohydrodynamics. Zbl 1404.65184Wu, Kailiang; Shu, Chi-Wang 5 2018 On local conservation of numerical methods for conservation laws. Zbl 1410.65327Shi, Cengke; Shu, Chi-Wang 5 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 4 2018 Discontinuous Galerkin methods for Maxwell’s equations in Drude metamaterials on unstructured meshes. Zbl 06887280Shi, Cengke; Li, Jichun; Shu, Chi-Wang 4 2018 Implicit positivity-preserving high-order discontinuous Galerkin methods for conservation laws. Zbl 1380.65285Qin, Tong; Shu, Chi-Wang 4 2018 Optimal error estimates of the semidiscrete central discontinuous Galerkin methods for linear hyperbolic equations. Zbl 1383.65108Liu, Yong; Shu, Chi-Wang; Zhang, Mengping 3 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 2 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 1 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 31 2017 Local discontinuous Galerkin method for the Keller-Segel chemotaxis model. Zbl 1384.92015Li, Xingjie Helen; Shu, Chi-Wang; Yang, Yang 17 2017 Optimal non-dissipative discontinuous Galerkin methods for Maxwell’s equations in Drude metamaterials. Zbl 1370.74143Li, Jichun; Shi, Cengke; Shu, Chi-Wang 17 2017 H(div) conforming and DG methods for incompressible Euler’s equations. Zbl 1433.76085Guzmán, Johnny; Shu, Chi-Wang; Sequeira, Filánder A. 11 2017 Stability of the fourth order Runge-Kutta method for time-dependent partial differential equations. Zbl 1381.65079Sun, Zheng; Shu, Chi-Wang 10 2017 A new troubled-cell indicator for discontinuous Galerkin methods for hyperbolic conservation laws. Zbl 1380.65262Fu, Guosheng; Shu, Chi-Wang 8 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 7 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 7 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 6 2017 A second-order asymptotic-preserving and positivity-preserving discontinuous Galerkin scheme for the Kerr-Debye model. Zbl 1360.65235Huang, Juntao; Shu, Chi-Wang 6 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 5 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 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 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 3 2017 Finite difference Hermite WENO schemes for the Hamilton-Jacobi equations. Zbl 1415.65204Zheng, Feng; Shu, Chi-Wang; Qiu, Jianxian 2 2017 Analysis of an embedded discontinuous Galerkin method with implicit-explicit time-marching for convection-diffusion problems. Zbl 1380.65261Fu, Guosheng; Shu, 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 Bound-preserving high order finite volume schemes for conservation laws and convection-diffusion equations. Zbl 1372.65251Shu, Chi-Wang 2 2017 Stability analysis and error estimates of Lax-Wendroff discontinuous Galerkin methods for linear conservation laws. Zbl 1373.65063Sun, Zheng; Shu, Chi-Wang 2 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 2 2017 Handbook on numerical methods for hyperbolic problems. Applied and modern issues. Zbl 1364.65001Abgrall, Rémi (ed.); Shu, Chi-Wang (ed.) 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 1 2017 An efficient class of WENO schemes with adaptive order. Zbl 1422.65146Balsara, Dinshaw S.; Garain, Sudip; Shu, Chi-Wang 48 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 32 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 32 2016 Bound-preserving discontinuous Galerkin methods for relativistic hydrodynamics. Zbl 1349.83037Qin, Tong; Shu, Chi-Wang; Yang, Yang 17 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 17 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 14 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 14 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 12 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 10 2016 A boundary condition-enforced immersed boundary method for compressible viscous flows. Zbl 1390.76504Qiu, Y. L.; Shu, C.; Wu, J.; Sun, Y.; Yang, L. M.; Guo, T. Q. 9 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 9 2016 Analysis of the local discontinuous Galerkin method for the drift-diffusion model of semiconductor devices. Zbl 1342.65183Liu, YunXian; 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 6 2016 Handbook of numerical methods for hyperbolic problems. Basic and fundamental issues. Zbl 1352.65001Abgrall, Remi (ed.); Shu, Chi-Wang (ed.) 5 2016 A new multiscale discontinuous Galerkin method for the one-dimensional stationary Schrödinger equation. Zbl 1342.65169Dong, Bo; Shu, Chi-Wang; Wang, Wei 4 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 3 2016 Convergence of discontinuous Galerkin schemes for front propagation with obstacles. Zbl 1353.65104Bokanowski, Olivier; Cheng, Yingda; Shu, Chi-Wang 3 2016 Three-dimensional ghost-fluid large-scale numerical investigation on air explosion. Zbl 1390.76635Wang, Cheng; Ding, JianXu; Shu, Chi-Wang; Li, Tao 2 2016 Discontinuous Galerkin methods for time-dependent convection dominated problems: basics, recent developments and comparison with other methods. Zbl 1357.65179Shu, Chi-Wang 2 2016 High order positivity-preserving discontinuous Galerkin methods for radiative transfer equations. Zbl 1351.65105Yuan, Daming; Cheng, Juan; Shu, Chi-Wang 2 2016 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 42 2015 An SPH model for multiphase flows with complex interfaces and large density differences. Zbl 1351.76231Chen, Z.; Zong, Z.; Liu, M. B.; Zou, L.; Li, H. T.; Shu, C. 31 2015 Superconvergence of discontinuous Galerkin methods for two-dimensional hyperbolic equations. Zbl 1328.65195Cao, Waixiang; Shu, Chi-Wang; Yang, Yang; Zhang, Zhimin 27 2015 A new class of central compact schemes with spectral-like resolution. II: Hybrid weighted nonlinear schemes. Zbl 1351.76170Liu, Xuliang; Zhang, Shuhai; Zhang, Hanxin; Shu, Chi-Wang 15 2015 Development and stability analysis of the inverse Lax-Wendroff boundary treatment for central compact schemes. Zbl 1311.65116Vilar, François; Shu, Chi-Wang 9 2015 A priori error estimates to smooth solutions of the third order Runge-Kutta discontinuous Galerkin method for symmetrizable systems of conservation laws. Zbl 1327.65193Luo, Juan; Shu, Chi-Wang; Zhang, Qiang 8 2015 Parallel adaptive mesh refinement method based on WENO finite difference scheme for the simulation of multi-dimensional detonation. Zbl 1349.76159Wang, Cheng; Dong, XinZhuang; Shu, Chi-Wang 7 2015 A simple weighted essentially non-oscillatory limiter for the correction procedure via reconstruction (CPR) framework. Zbl 1320.65114Du, Jie; Shu, Chi-Wang; Zhang, Mengping 7 2015 High order finite difference methods with subcell resolution for stiff multispecies discontinuity capturing. Zbl 1373.76197Wang, Wei; Shu, Chi-Wang; Yee, H. C.; Kotov, Dmitry V.; Sjögreen, Björn 6 2015 A three-dimensional explicit sphere function-based gas-kinetic flux solver for simulation of inviscid compressible flows. Zbl 1349.76751Yang, L. M.; Shu, C.; Wu, J. 6 2015 A simple weighted essentially non-oscillatory limiter for the correction procedure via reconstruction (CPR) framework on unstructured meshes. Zbl 1326.65130Du, Jie; Shu, Chi-Wang; Zhang, Mengping 6 2015 Recovering exponential accuracy in Fourier spectral methods involving piecewise smooth functions with unbounded derivative singularities. Zbl 1331.65145Chen, Zheng; Shu, Chi-Wang 2 2015 Numerical solution of the viscous surface wave with discontinuous Galerkin method. Zbl 1321.35143Wu, Lei; Shu, Chi-Wang 1 2015 High-order finite difference WENO schemes with positivity-preserving limiter for correlated random walk with density-dependent turning rates. Zbl 1318.65051Jiang, Yan; Shu, Chi-Wang; Zhang, Mengping 1 2015 A survey of high order schemes for the shallow water equations. Zbl 1324.76035Xing, Yulong; Shu, Chi-Wang 33 2014 Positivity-preserving Lagrangian scheme for multi-material compressible flow. Zbl 1349.76439Cheng, Juan; Shu, Chi-Wang 30 2014 Discontinuous Galerkin method for time-dependent problems: survey and recent developments. Zbl 1282.65122Shu, Chi-Wang 27 2014 Optimal energy conserving local discontinuous Galerkin methods for second-order wave equation in heterogeneous media. Zbl 1349.65446Chou, Ching-Shan; Shu, Chi-Wang; Xing, Yulong 23 2014 Error estimates for the third order explicit Runge-Kutta discontinuous Galerkin method for a linear hyperbolic equation in one-dimension with discontinuous initial data. Zbl 1293.65122Zhang, Qiang; Shu, Chi-Wang 16 2014 Free-stream preserving finite difference schemes on curvilinear meshes. Zbl 1292.65091Jiang, Yan; Shu, Chi-Wang; Zhang, Mengping 15 2014 A simple distribution function-based gas-kinetic scheme for simulation of viscous incompressible and compressible flows. Zbl 1351.76257Yang, L. M.; Shu, C.; Wu, J. 12 2014 Second order symmetry-preserving conservative Lagrangian scheme for compressible Euler equations in two-dimensional cylindrical coordinates. Zbl 1349.65367Cheng, Juan; Shu, Chi-Wang 11 2014 A discontinuous Galerkin scheme for front propagation with obstacles. Zbl 1291.65182Bokanowski, Olivier; Cheng, Yingda; Shu, Chi-Wang 7 2014 Multi-scale discontinuous Galerkin method for solving elliptic problems with curvilinear unidirectional rough coefficients. Zbl 1307.65171Zhang, Yifan; Wang, Wei; Guzmán, Johnny; Shu, Chi-Wang 5 2014 Recovering exponential accuracy from collocation point values of smooth functions with end-point singularities. Zbl 1311.65013Chen, Zheng; Shu, Chi-Wang 3 2014 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 56 2013 Positivity-preserving method for high-order conservative schemes solving compressible Euler equations. Zbl 1311.76088Hu, Xiangyu Y.; Adams, Nikolaus A.; Shu, Chi-Wang 45 2013 ...and 252 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 7,722 Authors 226 Shu, Chi-Wang 82 Dumbser, Michael 63 Qiu, Jianxian 46 Cockburn, Bernardo 46 Osher, Stanley Joel 43 Kurganov, Alexander 40 Adams, Nikolaus A. 39 Baccouch, Mahboub 38 Dawson, Clint N. 38 Xu, Yan 37 Li, Jichun 36 Toro, Eleuterio F. 35 Balsara, Dinshaw S. 35 Qiu, Jingmei 33 Don, Wai Sun 33 Liu, Hailiang 32 Cheng, Yingda 32 Mulet, Pep 32 Zhang, Mengping 31 Abgrall, Rémi 31 Dehghan Takht Fooladi, Mehdi 31 Hesthaven, Jan S. 30 Li, Fengyan 30 Xiao, Feng 29 Qian, Jianliang 29 Xing, Yulong 29 Xu, Kun 28 Bürger, Raimund 28 Fedkiw, Ronald P. 28 Zhu, Jun 27 Christlieb, Andrew J. 26 Gassner, Gregor J. 26 Munz, Claus-Dieter 26 Yu, Xijun 24 Jameson, Antony 24 Loubère, Raphaël 23 Chertock, Alina E. 23 Drikakis, Dimitris 23 Guermond, Jean-Luc 23 Karniadakis, George Em 23 Ren, Yuxin 23 van der Vegt, Jaap J. W. 22 Amat, Sergio P. 22 Gelb, Anne 22 Luo, Hong 22 Popov, Boyan 22 Ryan, Jennifer K. 22 Tang, Huazhong 22 Zhang, Yongtao 22 Zhang, Zhimin 21 Carpenter, Mark H. 21 Castro, Manuel J. 21 Gao, Zhen 21 Huang, Yunqing 21 Kuzmin, Dmitri 20 Adjerid, Slimane 20 Liu, Tiegang 20 Xia, Yinhua 20 Zhang, Qiang 19 Boscheri, Walter 19 Martínez Gamba, Irene 19 Gottlieb, Sigal 19 Seaïd, Mohammed 19 Xiong, Tao 18 Mishra, Siddhartha 18 Yee, Helen C. 17 Bassi, Francesco 17 Carrillo de la Plata, José Antonio 17 Deng, Xiaogang 17 Filbet, Francis 17 Gibou, Frédéric 17 Guo, Wei 17 Ketcheson, David I. 17 Kubatko, Ethan J. 17 Li, Gang 17 Pullin, Dale I. 17 Ricchiuto, Mario 17 Russo, Giovanni 17 Schötzau, Dominik 17 Sjogreen, Bjorn 17 Wei, LeiLei 17 Zhang, Xiangxiong 16 Donat, Rosa 16 Jung, Jae-Hun 16 Kang, Myungjoo 16 Parés Madroñal, Carlos 16 Tadmor, Eitan 16 Westerink, Joannes J. 15 Capdeville, Guy 15 Chandrashekar, Praveen 15 Ha, Youngsoo 15 Hu, Xiangyu Y. 15 Kesserwani, Georges 15 Kirby, Robert M. 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Académie des Sciences, Paris 7 Bulletin of the Brazilian Mathematical Society. New Series 7 Advances in Difference Equations 7 Communications in Applied and Industrial Mathematics 7 Journal of Theoretical Biology 7 SMAI Journal of Computational Mathematics 6 Applicable Analysis 6 Meccanica 6 Discrete and Continuous Dynamical Systems 6 Doklady Mathematics 6 Nonlinear Analysis. Real World Applications 6 Communications in Applied Mathematics and Computational Science 6 Networks and Heterogeneous Media 5 Theoretical and Computational Fluid Dynamics 5 Studies in Applied Mathematics 5 RAIRO. 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