Error estimates to smooth solutions of semi-discrete discontinuous Galerkin methods with quadrature rules for scalar conservation laws

Juntao Huang; Chi-Wang Shu

doi:10.1002/num.22089

Error estimates to smooth solutions of semi-discrete discontinuous Galerkin methods with quadrature rules for scalar conservation laws

Numerical Methods for Partial Differential Equations ◽

10.1002/num.22089 ◽

2016 ◽

Vol 33 (2) ◽

pp. 467-488 ◽

Cited By ~ 5

Author(s):

Juntao Huang ◽

Chi-Wang Shu

Keyword(s):

Conservation Laws ◽

Error Estimates ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Quadrature Rules ◽

Galerkin Methods ◽

Smooth Solutions ◽

Scalar Conservation Laws ◽

Scalar Conservation

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Error Estimates to Smooth Solutions of Runge--Kutta Discontinuous Galerkin Methods for Scalar Conservation Laws

SIAM Journal on Numerical Analysis ◽

10.1137/s0036142902404182 ◽

2004 ◽

Vol 42 (2) ◽

pp. 641-666 ◽

Cited By ~ 109

Author(s):

Qiang Zhang ◽

Chi-Wang Shu

Keyword(s):

Conservation Laws ◽

Error Estimates ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Smooth Solutions ◽

Scalar Conservation Laws ◽

Runge Kutta ◽

Scalar Conservation

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Discontinuous Galerkin Methods for Nonlinear Scalar Conservation Laws: Generalized Local Lax--Friedrichs Numerical Fluxes

SIAM Journal on Numerical Analysis ◽

10.1137/19m1243798 ◽

2020 ◽

Vol 58 (1) ◽

pp. 1-20 ◽

Cited By ~ 1

Author(s):

Jia Li ◽

Dazhi Zhang ◽

Xiong Meng ◽

Boying Wu ◽

Qiang Zhang

Keyword(s):

Conservation Laws ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Scalar Conservation Laws ◽

Numerical Fluxes ◽

Scalar Conservation ◽

Nonlinear Scalar Conservation Laws

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Pointwise Error Estimates for Scalar Conservation Laws with Piecewise Smooth Solutions

SIAM Journal on Numerical Analysis ◽

10.1137/s0036142998333997 ◽

1999 ◽

Vol 36 (6) ◽

pp. 1739-1758 ◽

Cited By ~ 19

Author(s):

Eitan Tadmor ◽

Tao Tang

Keyword(s):

Conservation Laws ◽

Error Estimates ◽

Piecewise Smooth ◽

Smooth Solutions ◽

Scalar Conservation Laws ◽

Pointwise Error ◽

Scalar Conservation ◽

Pointwise Error Estimates

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Stability analysis and error estimates of Lax–Wendroff discontinuous Galerkin methods for linear conservation laws

ESAIM Mathematical Modelling and Numerical Analysis ◽

10.1051/m2an/2016049 ◽

2017 ◽

Vol 51 (3) ◽

pp. 1063-1087 ◽

Cited By ~ 2

Author(s):

Zheng Sun ◽

Chi-Wang Shu

Keyword(s):

Stability Analysis ◽

Conservation Laws ◽

Error Estimates ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods

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Entropy stable high order discontinuous Galerkin methods with suitable quadrature rules for hyperbolic conservation laws

Journal of Computational Physics ◽

10.1016/j.jcp.2017.05.025 ◽

2017 ◽

Vol 345 ◽

pp. 427-461 ◽

Cited By ~ 62

Author(s):

Tianheng Chen ◽

Chi-Wang Shu

Keyword(s):

Conservation Laws ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Hyperbolic Conservation Laws ◽

High Order ◽

Quadrature Rules ◽

Galerkin Methods ◽

Hyperbolic Conservation ◽

Entropy Stable

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Maximum-Principle-Satisfying and Positivity-Preserving High Order Central Discontinuous Galerkin Methods for Hyperbolic Conservation Laws

SIAM Journal on Scientific Computing ◽

10.1137/16m1070001 ◽

2016 ◽

Vol 38 (6) ◽

pp. A3720-A3740 ◽

Cited By ~ 10

Author(s):

Maojun Li ◽

Fengyan Li ◽

Zhen Li ◽

Liwei Xu

Keyword(s):

Maximum Principle ◽

Conservation Laws ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Hyperbolic Conservation Laws ◽

Galerkin Methods ◽

Positivity Preserving ◽

Hyperbolic Conservation ◽

Central Discontinuous Galerkin ◽

Central Discontinuous Galerkin Methods

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A priori error estimates for numerical methods for scalar conservation laws. Part I: The general approach

Mathematics of Computation ◽

10.1090/s0025-5718-96-00701-6 ◽

1996 ◽

Vol 65 (214) ◽

pp. 533-574 ◽

Cited By ~ 32

Author(s):

Bernardo Cockburn ◽

Pierre-Alain Gremaud

Keyword(s):

Numerical Methods ◽

Conservation Laws ◽

Error Estimates ◽

A Priori ◽

A Priori Error Estimates ◽

Scalar Conservation Laws ◽

Priori Error Estimates ◽

Scalar Conservation

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Comparison of Finite Volume and Discontinuous Galerkin Methods of Higher Order for Systems of Conservation Laws in Multiple Space Dimensions

Geometric Analysis and Nonlinear Partial Differential Equations ◽

10.1007/978-3-642-55627-2_30 ◽

2003 ◽

pp. 573-589 ◽

Cited By ~ 3

Author(s):

A. Dedner ◽

D. Kröner ◽

C. Rohde ◽

T. Schnitzer ◽

M. Wesenberg

Keyword(s):

Conservation Laws ◽

Discontinuous Galerkin ◽

Finite Volume ◽

Discontinuous Galerkin Methods ◽

Higher Order ◽

Galerkin Methods ◽

Systems Of Conservation Laws

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A Family of Characteristic Discontinuous Galerkin Methods for Transient Advection-Diffusion Equations and Their Optimal-Order L^2 Error Estimates

Communications in Computational Physics ◽

10.4208/cicp.2009.v6.p203 ◽

2009 ◽

pp. 203-230 ◽

Cited By ~ 8

Author(s):

Kaixin Wang ◽

Hong Wang ◽

Mohamed Al-Lawatia ◽

Hongxing Rui

Keyword(s):

Error Estimates ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Diffusion Equations ◽

Optimal Order ◽

Galerkin Methods ◽

Advection Diffusion

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Unconditional stability and optimal error estimates of discontinuous Galerkin methods for the second-order wave equation

Applicable Analysis ◽

10.1080/00036811.2019.1636968 ◽

2019 ◽

pp. 1-15 ◽

Cited By ~ 1

Author(s):

Limin He ◽

Weimin Han ◽

Fei Wang ◽

Wentao Cai

Keyword(s):

Wave Equation ◽

Error Estimates ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Unconditional Stability ◽

Second Order ◽

Optimal Error Estimates ◽

Galerkin Methods ◽

Optimal Error ◽

Second Order Wave Equation

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