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 ◽

Download Full-text

Superconvergence of Discontinuous Galerkin Methods for Scalar Nonlinear Conservation Laws in One Space Dimension

SIAM Journal on Numerical Analysis ◽

10.1137/110857635 ◽

2012 ◽

Vol 50 (5) ◽

pp. 2336-2356 ◽

Author(s):

Xiong Meng ◽

Chi-Wang Shu ◽

Qiang Zhang ◽

Boying Wu

Keyword(s):

Conservation Laws ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Space Dimension ◽

Galerkin Methods ◽

Nonlinear Conservation Laws ◽

One Space Dimension

Download Full-text

Error Control for a Class of Runge–Kutta Discontinuous Galerkin Methods for Nonlinear Conservation Laws

SIAM Journal on Numerical Analysis ◽

10.1137/050624248 ◽

2007 ◽

Vol 45 (2) ◽

pp. 514-538 ◽

Author(s):

Andreas Dedner ◽

Charalambos Makridakis ◽

Mario Ohlberger

Keyword(s):

Conservation Laws ◽

Discontinuous Galerkin ◽

Error Control ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Nonlinear Conservation Laws ◽

Download Full-text

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 ◽

Download Full-text

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 ◽

Download Full-text

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 ◽

Download Full-text

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

Download Full-text

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 ◽

Download Full-text

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

Download Full-text

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

Download Full-text

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 ◽

Download Full-text