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

Ruihan Guo; Francis Filbet; Yan Xu

doi:10.1007/s10915-016-0170-4

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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High Order Local Discontinuous Galerkin Methods for the Allen-Cahn Equation: Analysis and Simulation

Journal of Computational Mathematics ◽

10.4208/jcm.1510-m2014-0002 ◽

2016 ◽

Vol 34 (2) ◽

pp. 135-158 ◽

Cited By ~ 7

Author(s):

Ruihan Guo

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

High Order ◽

Galerkin Methods ◽

Cahn Equation ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods ◽

Equation Analysis

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Efficient time discretization for local discontinuous Galerkin methods

Discrete & Continuous Dynamical Systems - B ◽

10.3934/dcdsb.2007.8.677 ◽

2007 ◽

Vol 8 (3) ◽

pp. 677-693 ◽

Cited By ~ 40

Author(s):

Yinhua Xia ◽

◽

Yan Xu ◽

Chi-Wang Shu ◽

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Time Discretization ◽

Galerkin Methods ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods

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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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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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Energy conserving local discontinuous Galerkin methods for the improved Boussinesq equation

Journal of Computational Physics ◽

10.1016/j.jcp.2019.109002 ◽

2020 ◽

Vol 401 ◽

pp. 109002 ◽

Cited By ~ 4

Author(s):

Xiaole Li ◽

Weizhou Sun ◽

Yulong Xing ◽

Ching-Shan Chou

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Boussinesq Equation ◽

Galerkin Methods ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods ◽

Energy Conserving

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Local discontinuous Galerkin methods for the generalized Zakharov system

Journal of Computational Physics ◽

10.1016/j.jcp.2009.10.029 ◽

2010 ◽

Vol 229 (4) ◽

pp. 1238-1259 ◽

Cited By ~ 23

Author(s):

Yinhua Xia ◽

Yan Xu ◽

Chi-Wang Shu

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Zakharov System ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods

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