Stability and Error Estimates of Local Discontinuous Galerkin Methods with Implicit-Explicit Time-Marching for Advection-Diffusion Problems

SIAM Journal on Numerical Analysis ◽

10.1137/140956750 ◽

2015 ◽

Vol 53 (1) ◽

pp. 206-227 ◽

Author(s):

Haijin Wang ◽

Chi-Wang Shu ◽

Qiang Zhang

Keyword(s):

Error Estimates ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Local Discontinuous Galerkin ◽

Advection Diffusion ◽

Local Discontinuous Galerkin Methods ◽

Time Marching ◽

Diffusion Problems

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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 ◽

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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Stability analysis and error estimates of local discontinuous Galerkin methods with implicit-explicit time-marching for the time-dependent fourth order PDEs

ESAIM Mathematical Modelling and Numerical Analysis ◽

10.1051/m2an/2017017 ◽

2017 ◽

Vol 51 (5) ◽

pp. 1931-1955 ◽

Author(s):

Haijin Wang ◽

Qiang Zhang ◽

Chi-Wang Shu

Keyword(s):

Stability Analysis ◽

Error Estimates ◽

Discontinuous Galerkin ◽

Fourth Order ◽

Discontinuous Galerkin Methods ◽

Time Dependent ◽

Galerkin Methods ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods ◽

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Stability analysis and error estimates of local discontinuous Galerkin methods with implicit–explicit time-marching for nonlinear convection–diffusion problems

Applied Mathematics and Computation ◽

10.1016/j.amc.2015.02.067 ◽

2016 ◽

Vol 272 ◽

pp. 237-258 ◽

Author(s):

Haijin Wang ◽

Chi-Wang Shu ◽

Qiang Zhang

Keyword(s):

Stability Analysis ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Nonlinear Convection ◽

Convection Diffusion ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods ◽

Time Marching ◽

Diffusion Problems

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Stability analysis and error estimates of local discontinuous Galerkin methods with semi-implicit spectral deferred correction time-marching for the Allen–Cahn equation

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2020.112857 ◽

2020 ◽

Vol 376 ◽

pp. 112857

Author(s):

Fengna Yan ◽

Yan Xu

Keyword(s):

Stability Analysis ◽

Error Estimates ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Cahn Equation ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods ◽

Time Marching ◽

Spectral Deferred Correction

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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 ◽

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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Stability analysis and error estimates of local discontinuous Galerkin methods for convection–diffusion equations on overlapping meshes

BIT Numerical Mathematics ◽

10.1007/s10543-019-00757-4 ◽

2019 ◽

Vol 59 (4) ◽

pp. 853-876 ◽

Author(s):

Jie Du ◽

Yang Yang ◽

Eric Chung

Keyword(s):

Stability Analysis ◽

Error Estimates ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Diffusion Equations ◽

Galerkin Methods ◽

Convection Diffusion ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods

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Local discontinuous Galerkin methods with explicit Runge-Kutta time marching for nonlinear carburizing model

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.4898 ◽

2018 ◽

Vol 41 (12) ◽

pp. 4376-4390 ◽

Author(s):

Chenghui Xia ◽

Ying Li ◽

Haijin Wang

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods ◽

Time Marching ◽

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Local discontinuous Galerkin methods with implicit-explicit multistep time-marching for solving the nonlinear Cahn-Hilliard equation

Journal of Computational Physics ◽

10.1016/j.jcp.2019.05.040 ◽

2019 ◽

Vol 394 ◽

pp. 719-731 ◽

Author(s):

Hui Shi ◽

Ying Li

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Hilliard Equation ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods ◽

Time Marching ◽

Cahn Hilliard Equation

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Error estimates for a class of energy- and Hamiltonian-preserving local discontinuous Galerkin methods for the Klein–Gordon–Schrödinger equations

Journal of Applied Mathematics and Computing ◽

10.1007/s12190-019-01289-4 ◽

2019 ◽

Vol 62 (1-2) ◽

pp. 377-424 ◽

Author(s):

He Yang

Keyword(s):

Error Estimates ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Schrodinger Equations ◽

Galerkin Methods ◽

Schrödinger Equations ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods ◽

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Local discontinuous Galerkin methods with implicit-explicit time-marching for time-dependent incompressible fluid flow

Mathematics of Computation ◽

10.1090/mcom/3312 ◽

2018 ◽

Vol 88 (315) ◽

pp. 91-121 ◽

Author(s):

Haijin Wang ◽

Yunxian Liu ◽

Qiang Zhang ◽

Chi-Wang Shu

Keyword(s):

Incompressible Fluid ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Time Dependent ◽

Galerkin Methods ◽

Incompressible Fluid Flow ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods ◽

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