Local discontinuous Galerkin methods for two classes of two-dimensional nonlinear wave equations

Yan Xu; Chi-Wang Shu

doi:10.1016/j.physd.2005.06.007

Local discontinuous Galerkin methods for two classes of two-dimensional nonlinear wave equations

Physica D Nonlinear Phenomena ◽

10.1016/j.physd.2005.06.007 ◽

2005 ◽

Vol 208 (1-2) ◽

pp. 21-58 ◽

Cited By ~ 51

Author(s):

Yan Xu ◽

Chi-Wang Shu

Keyword(s):

Discontinuous Galerkin ◽

Nonlinear Wave ◽

Wave Equations ◽

Discontinuous Galerkin Methods ◽

Nonlinear Wave Equations ◽

Galerkin Methods ◽

Two Dimensional ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods

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Local discontinuous Galerkin methods for moment models in device simulations: Performance assessment and two-dimensional results

Applied Numerical Mathematics ◽

10.1016/j.apnum.2006.07.027 ◽

2007 ◽

Vol 57 (5-7) ◽

pp. 629-645 ◽

Cited By ~ 15

Author(s):

Yunxian Liu ◽

Chi-Wang Shu

Keyword(s):

Performance Assessment ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Two Dimensional ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods ◽

Moment Models

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Local Discontinuous Galerkin Methods with Generalized Alternating Numerical Fluxes for Two-dimensional Linear Sobolev Equation

Journal of Scientific Computing ◽

10.1007/s10915-018-0819-2 ◽

2018 ◽

Vol 78 (3) ◽

pp. 1660-1690

Author(s):

Di Zhao ◽

Qiang Zhang

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Two Dimensional ◽

Sobolev Equation ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods ◽

Numerical Fluxes

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Local Discontinuous Galerkin Methods for the Two-Dimensional Camassa–Holm Equation

Communications in Mathematics and Statistics ◽

10.1007/s40304-018-0140-2 ◽

2018 ◽

Vol 6 (3) ◽

pp. 359-388

Author(s):

Tian Ma ◽

Yan Xu

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Two Dimensional ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods ◽

Holm Equation

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High-Order Accurate Runge-Kutta (Local) Discontinuous Galerkin Methods for One- and Two-Dimensional Fractional Diffusion Equations

Numerical Mathematics Theory Methods and Applications ◽

10.4208/nmtma.2012.m1107 ◽

2012 ◽

Vol 5 (3) ◽

pp. 333-358 ◽

Cited By ~ 30

Author(s):

Xia Ji and Huazhong Tang

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Fractional Diffusion ◽

High Order ◽

Diffusion Equations ◽

Galerkin Methods ◽

Two Dimensional ◽

Fractional Diffusion Equations ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods

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Optimal Error Estimates of the Semidiscrete Local Discontinuous Galerkin Methods for High Order Wave Equations

SIAM Journal on Numerical Analysis ◽

10.1137/11082258x ◽

2012 ◽

Vol 50 (1) ◽

pp. 79-104 ◽

Cited By ~ 46

Author(s):

Yan Xu ◽

Chi-Wang Shu

Keyword(s):

Error Estimates ◽

Discontinuous Galerkin ◽

Wave Equations ◽

Discontinuous Galerkin Methods ◽

High Order ◽

Optimal Error Estimates ◽

Galerkin Methods ◽

Optimal Error ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods

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Local Discontinuous Galerkin Methods to a Dispersive System of KdV-Type Equations

Journal of Scientific Computing ◽

10.1007/s10915-020-01370-2 ◽

2021 ◽

Vol 86 (1) ◽

Author(s):

Chao Zhang ◽

Yan Xu ◽

Yinhua Xia

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods ◽

Dispersive System ◽

Kdv Type Equations

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Local discontinuous Galerkin methods for the Kuramoto–Sivashinsky equations and the Ito-type coupled KdV equations

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/j.cma.2005.06.021 ◽

2006 ◽

Vol 195 (25-28) ◽

pp. 3430-3447 ◽

Cited By ~ 66

Author(s):

Yan Xu ◽

Chi-Wang Shu

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Local Discontinuous Galerkin ◽

Kdv Equations ◽

Local Discontinuous Galerkin Methods ◽

Coupled Kdv Equations

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Local discontinuous Galerkin methods with implicit-explicit time-marching for multi-dimensional convection-diffusion problems

ESAIM Mathematical Modelling and Numerical Analysis ◽

10.1051/m2an/2015068 ◽

2016 ◽

Vol 50 (4) ◽

pp. 1083-1105 ◽

Cited By ~ 21

Author(s):

Haijin Wang ◽

Shiping Wang ◽

Qiang Zhang ◽

Chi-Wang Shu

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Convection Diffusion ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods ◽

Time Marching ◽

Diffusion Problems

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Efficient High Order Semi-implicit Time Discretization and Local Discontinuous Galerkin Methods for Highly Nonlinear PDEs

Journal of Scientific Computing ◽

10.1007/s10915-016-0170-4 ◽

2016 ◽

Vol 68 (3) ◽

pp. 1029-1054 ◽

Cited By ~ 7

Author(s):

Ruihan Guo ◽

Francis Filbet ◽

Yan Xu

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Time Discretization ◽

High Order ◽

Nonlinear Pdes ◽

Implicit Time ◽

Galerkin Methods ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods ◽

Highly Nonlinear

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Implicit–Explicit Local Discontinuous Galerkin Methods with Generalized Alternating Numerical Fluxes for Convection–Diffusion Problems

Journal of Scientific Computing ◽

10.1007/s10915-019-01072-4 ◽

2019 ◽

Vol 81 (3) ◽

pp. 2080-2114 ◽

Cited By ~ 4

Author(s):

Haijin Wang ◽

Qiang Zhang ◽

Chi-Wang Shu

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Convection Diffusion ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods ◽

Numerical Fluxes ◽

Diffusion Problems

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