The L$^2$-norm Stability Analysis of Runge--Kutta Discontinuous Galerkin Methods for Linear Hyperbolic Equations

SIAM Journal on Numerical Analysis ◽

10.1137/18m1230700 ◽

2019 ◽

Vol 57 (4) ◽

pp. 1574-1601 ◽

Author(s):

Yuan Xu ◽

Qiang Zhang ◽

Chi-wang Shu ◽

Haijin Wang

Keyword(s):

Stability Analysis ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Hyperbolic Equations ◽

Galerkin Methods ◽

Runge Kutta ◽

Linear Hyperbolic Equations

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Error Estimate of the Fourth-Order Runge--Kutta Discontinuous Galerkin Methods for Linear Hyperbolic Equations

SIAM Journal on Numerical Analysis ◽

10.1137/19m1280077 ◽

2020 ◽

Vol 58 (5) ◽

pp. 2885-2914

Author(s):

Yuan Xu ◽

Chi-Wang Shu ◽

Qiang Zhang

Keyword(s):

Error Estimate ◽

Discontinuous Galerkin ◽

Fourth Order ◽

Discontinuous Galerkin Methods ◽

Hyperbolic Equations ◽

Galerkin Methods ◽

Runge Kutta ◽

Linear Hyperbolic Equations

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Stabilized discontinuous Galerkin methods for scalar linear hyperbolic equations

Applied Mathematics and Computation ◽

10.1016/j.amc.2006.05.047 ◽

2006 ◽

Vol 182 (2) ◽

pp. 1623-1628

Author(s):

Mi-Young Kim

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Hyperbolic Equations ◽

Galerkin Methods ◽

Linear Hyperbolic Equations

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Superconvergence of Arbitrary Lagrangian--Eulerian Discontinuous Galerkin Methods for Linear Hyperbolic Equations

SIAM Journal on Numerical Analysis ◽

10.1137/18m122916x ◽

2019 ◽

Vol 57 (5) ◽

pp. 2142-2165 ◽

Author(s):

Qi Tao ◽

Yan Xu

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Hyperbolic Equations ◽

Galerkin Methods ◽

Arbitrary Lagrangian Eulerian ◽

Linear Hyperbolic Equations

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Sub-Optimal Convergence of Discontinuous Galerkin Methods with Central Fluxes for Linear Hyperbolic Equations with Even Degree Polynomial Approximations

Journal of Computational Mathematics ◽

10.4208/jcm.2002-m2019-0305 ◽

2021 ◽

Vol 39 (4) ◽

pp. 629-648

Author(s):

global sci

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Hyperbolic Equations ◽

Galerkin Methods ◽

Degree Polynomial ◽

Optimal Convergence ◽

Polynomial Approximations ◽

Linear Hyperbolic Equations

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Superconvergence of Discontinuous Galerkin Methods for Linear Hyperbolic Equations

SIAM Journal on Numerical Analysis ◽

10.1137/130946873 ◽

2014 ◽

Vol 52 (5) ◽

pp. 2555-2573 ◽

Author(s):

Waixiang Cao ◽

Zhimin Zhang ◽

Qingsong Zou

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Hyperbolic Equations ◽

Galerkin Methods ◽

Linear Hyperbolic Equations

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Optimal Error Estimates of the Semidiscrete Central Discontinuous Galerkin Methods for Linear Hyperbolic Equations

SIAM Journal on Numerical Analysis ◽

10.1137/16m1089484 ◽

2018 ◽

Vol 56 (1) ◽

pp. 520-541 ◽

Author(s):

Yong Liu ◽

Chi-Wang Shu ◽

Mengping Zhang

Keyword(s):

Error Estimates ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Hyperbolic Equations ◽

Optimal Error Estimates ◽

Galerkin Methods ◽

Optimal Error ◽

Central Discontinuous Galerkin ◽

Central Discontinuous Galerkin Methods ◽

Linear Hyperbolic Equations

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Bound-preserving modified exponential Runge–Kutta discontinuous Galerkin methods for scalar hyperbolic equations with stiff source terms

Journal of Computational Physics ◽

10.1016/j.jcp.2018.01.051 ◽

2018 ◽

Vol 361 ◽

pp. 111-135 ◽

Author(s):

Juntao Huang ◽

Chi-Wang Shu

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Hyperbolic Equations ◽

Galerkin Methods ◽

Source Terms ◽

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Superconvergence of Energy-Conserving Discontinuous Galerkin Methods for Linear Hyperbolic Equations

Communications on Applied Mathematics and Computation ◽

10.1007/s42967-019-0006-y ◽

2019 ◽

Vol 1 (1) ◽

pp. 101-116 ◽

Author(s):

Yong Liu ◽

Chi-Wang Shu ◽

Mengping Zhang

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Hyperbolic Equations ◽

Galerkin Methods ◽

Energy Conserving ◽

Linear Hyperbolic Equations

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Superconvergence of Discontinuous Galerkin methods based on upwind-biased fluxes for 1D linear hyperbolic equations

ESAIM Mathematical Modelling and Numerical Analysis ◽

10.1051/m2an/2016026 ◽

2017 ◽

Vol 51 (2) ◽

pp. 467-486 ◽

Author(s):

Waixiang Cao ◽

Dongfang Li ◽

Yang Yang ◽

Zhimin Zhang

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Hyperbolic Equations ◽

Galerkin Methods ◽

Linear Hyperbolic Equations

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Optimal error estimates for discontinuous Galerkin methods based on upwind-biased fluxes for linear hyperbolic equations

Mathematics of Computation ◽

10.1090/mcom/3022 ◽

2015 ◽

Vol 85 (299) ◽

pp. 1225-1261 ◽

Author(s):

Xiong Meng ◽

Chi-Wang Shu ◽

Boying Wu

Keyword(s):

Error Estimates ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Hyperbolic Equations ◽

Optimal Error Estimates ◽

Galerkin Methods ◽

Optimal Error ◽

Linear Hyperbolic Equations

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