Review Article:Review of Entropy Stable Discontinuous Galerkin Methods for Systems of Conservation Laws on Unstructured Simplex Meshes

CSIAM Transactions on Applied Mathematics ◽

10.4208/csiam-am.2020-0003 ◽

2020 ◽

Vol 1 (1) ◽

pp. 1-52 ◽

Author(s):

Tianheng Chen & Chi-Wang Shu

Keyword(s):

Conservation Laws ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Systems Of Conservation Laws ◽

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Review of Entropy Stable Discontinuous Galerkin Methods for Systems of Conservation Laws on Unstructured Simplex Meshes

CSIAM Transactions on Applied Mathematics ◽

10.4208/csam.2020-0003 ◽

2020 ◽

Vol 1 (1) ◽

pp. 1-52

Author(s):

global sci

Keyword(s):

Conservation Laws ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Systems Of Conservation Laws ◽

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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 ◽

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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High-order discontinuous Galerkin methods with Lagrange multiplier for hyperbolic systems of conservation laws

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2017.02.039 ◽

2017 ◽

Vol 73 (9) ◽

pp. 1945-1974 ◽

Author(s):

Mi-Young Kim ◽

Eun-Jae Park ◽

Jaemin Shin

Keyword(s):

Conservation Laws ◽

Discontinuous Galerkin ◽

Lagrange Multiplier ◽

Discontinuous Galerkin Methods ◽

Hyperbolic Systems ◽

Galerkin Methods ◽

Systems Of Conservation Laws

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Stabilization for discontinuous Galerkin methods applied to systems of conservation laws

Hyperbolic Problems: Theory, Numerics and Applications - Proceedings of Symposia in Applied Mathematics ◽

10.1090/psapm/067.1/2605223 ◽

2009 ◽

pp. 253-268

Author(s):

Andreas Dedner ◽

Robert Klöfkorn

Keyword(s):

Conservation Laws ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Systems Of Conservation Laws

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Entropy Stable Discontinuous Galerkin Methods for Nonlinear Conservation Laws on Networks and Multi-Dimensional Domains

Journal of Scientific Computing ◽

10.1007/s10915-021-01464-5 ◽

2021 ◽

Vol 87 (3) ◽

Author(s):

Xinhui Wu ◽

Jesse Chan

Keyword(s):

Conservation Laws ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Nonlinear Conservation Laws ◽

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Simplified Discontinuous Galerkin Methods for Systems of Conservation Laws with Convex Extension

Lecture Notes in Computational Science and Engineering - Discontinuous Galerkin Methods ◽

10.1007/978-3-642-59721-3_3 ◽

2000 ◽

pp. 63-75 ◽

Author(s):

Timothy J. Barth

Keyword(s):

Conservation Laws ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Systems Of Conservation Laws

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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 ◽

Author(s):

Tianheng Chen ◽

Chi-Wang Shu

Keyword(s):

Conservation Laws ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Hyperbolic Conservation Laws ◽

Quadrature Rules ◽

Galerkin Methods ◽

Hyperbolic Conservation ◽

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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 ◽

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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On discretely entropy conservative and entropy stable discontinuous Galerkin methods

Journal of Computational Physics ◽

10.1016/j.jcp.2018.02.033 ◽

2018 ◽

Vol 362 ◽

pp. 346-374 ◽

Author(s):

Jesse Chan

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

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Devising discontinuous Galerkin methods for non-linear hyperbolic conservation laws

Journal of Computational and Applied Mathematics ◽

10.1016/s0377-0427(00)00512-4 ◽

2001 ◽

Vol 128 (1-2) ◽

pp. 187-204 ◽

Author(s):

Bernardo Cockburn

Keyword(s):

Conservation Laws ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Hyperbolic Conservation Laws ◽

Galerkin Methods ◽

Hyperbolic Conservation ◽

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