Optimal error estimate of the local discontinuous Galerkin methods based on the generalized alternating numerical fluxes for nonlinear convection–diffusion equations

Numerical Algorithms ◽

10.1007/s11075-018-0529-8 ◽

2018 ◽

Vol 80 (4) ◽

pp. 1329-1359 ◽

Author(s):

Yao Cheng

Keyword(s):

Discontinuous Galerkin Methods ◽

Diffusion Equations ◽

Optimal Error Estimate ◽

Galerkin Methods ◽

Optimal Error ◽

Nonlinear Convection ◽

Convection Diffusion ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods ◽

Numerical Fluxes

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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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Superconvergence of local discontinuous Galerkin methods for one-dimensional convection–diffusion equations

Computers & Structures ◽

10.1016/j.compstruc.2008.11.012 ◽

2009 ◽

Vol 87 (11-12) ◽

pp. 630-641 ◽

Author(s):

Yingda Cheng ◽

Chi-Wang Shu

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Diffusion Equations ◽

Galerkin Methods ◽

One Dimensional ◽

Convection Diffusion ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods

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The optimal error estimate and superconvergence of the local discontinuous Galerkin methods for one-dimensional linear fifth order time dependent equations

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2016.05.030 ◽

2016 ◽

Vol 72 (3) ◽

pp. 687-703 ◽

Author(s):

Hui Bi ◽

Chengeng Qian ◽

Yang Sun

Keyword(s):

Error Estimate ◽

Discontinuous Galerkin Methods ◽

Time Dependent ◽

Optimal Error Estimate ◽

Galerkin Methods ◽

Optimal Error ◽

One Dimensional ◽

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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Superconvergence of local discontinuous Galerkin methods with generalized alternating fluxes for 1D linear convection-diffusion equations

Science China Mathematics ◽

10.1007/s11425-019-1627-7 ◽

2020 ◽

Author(s):

Xiaobin Liu ◽

Dazhi Zhang ◽

Xiong Meng ◽

Boying Wu

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Diffusion Equations ◽

Galerkin Methods ◽

Convection Diffusion ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods

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Superconvergence analysis of local discontinuous Galerkin methods for linear convection–diffusion equations in one space dimension

Computational and Applied Mathematics ◽

10.1007/s40314-019-0777-9 ◽

2019 ◽

Vol 38 (1) ◽

Author(s):

Jun Zhang ◽

Xiangling Chen

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Space Dimension ◽

Diffusion Equations ◽

Galerkin Methods ◽

Convection Diffusion ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods ◽

One Space Dimension

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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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Local Discontinuous Galerkin methods for fractional diffusion equations

ESAIM Mathematical Modelling and Numerical Analysis ◽

10.1051/m2an/2013091 ◽

2013 ◽

Vol 47 (6) ◽

pp. 1845-1864 ◽

Author(s):

W.H. Deng ◽

J.S. Hesthaven

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Fractional Diffusion ◽

Diffusion Equations ◽

Galerkin Methods ◽

Fractional Diffusion Equations ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods

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Local Discontinuous Galerkin Methods with Novel Basis for Fractional Diffusion Equations with Non-smooth Solutions

Communications on Applied Mathematics and Computation ◽

10.1007/s42967-020-00104-3 ◽

2021 ◽

Author(s):

Liyao Lyu ◽

Zheng Chen

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Fractional Diffusion ◽

Diffusion Equations ◽

Galerkin Methods ◽

Smooth Solutions ◽

Fractional Diffusion Equations ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods

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