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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High Order Cut Discontinuous Galerkin Methods for Hyperbolic Conservation Laws in One Space Dimension

SIAM Journal on Scientific Computing ◽

10.1137/20m1349060 ◽

2021 ◽

Vol 43 (4) ◽

pp. A2404-A2424

Author(s):

Pei Fu ◽

Gunilla Kreiss

Keyword(s):

Conservation Laws ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Hyperbolic Conservation Laws ◽

Space Dimension ◽

Galerkin Methods ◽

Hyperbolic Conservation ◽

One Space Dimension

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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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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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Aspects of discontinuous Galerkin methods for hyperbolic conservation laws

Finite Elements in Analysis and Design ◽

10.1016/s0168-874x(02)00083-5 ◽

2002 ◽

Vol 38 (10) ◽

pp. 889-908 ◽

Author(s):

Joseph E. Flaherty ◽

Lilia Krivodonova ◽

Jean-Francois Remacle ◽

Mark S. Shephard

Keyword(s):

Conservation Laws ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Hyperbolic Conservation Laws ◽

Galerkin Methods ◽

Hyperbolic Conservation

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Shock detection and limiting with discontinuous Galerkin methods for hyperbolic conservation laws

Applied Numerical Mathematics ◽

10.1016/j.apnum.2003.11.002 ◽

2004 ◽

Vol 48 (3-4) ◽

pp. 323-338 ◽

Author(s):

L. Krivodonova ◽

J. Xin ◽

J.-F. Remacle ◽

N. Chevaugeon ◽

J.E. Flaherty

Keyword(s):

Conservation Laws ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Hyperbolic Conservation Laws ◽

Galerkin Methods ◽

Hyperbolic Conservation ◽

Shock Detection

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Divided difference estimates and accuracy enhancement of discontinuous Galerkin methods for nonlinear symmetric systems of hyperbolic conservation laws

IMA Journal of Numerical Analysis ◽

10.1093/imanum/drw072 ◽

2017 ◽

Vol 38 (1) ◽

pp. 125-155 ◽

Author(s):

Xiong Meng ◽

Jennifer K Ryan

Keyword(s):

Conservation Laws ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Hyperbolic Conservation Laws ◽

Divided Difference ◽

Galerkin Methods ◽

Accuracy Enhancement ◽

Hyperbolic Conservation ◽

Symmetric Systems

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Discontinuous Galerkin methods for nonlinear scalar hyperbolic conservation laws: divided difference estimates and accuracy enhancement

Numerische Mathematik ◽

10.1007/s00211-016-0833-y ◽

2016 ◽

Vol 136 (1) ◽

pp. 27-73 ◽

Author(s):

Xiong Meng ◽

Jennifer K. Ryan

Keyword(s):

Conservation Laws ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Hyperbolic Conservation Laws ◽

Divided Difference ◽

Galerkin Methods ◽

Accuracy Enhancement ◽

Hyperbolic Conservation

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Approximate Lax–Wendroff discontinuous Galerkin methods for hyperbolic conservation laws

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2017.06.019 ◽

2017 ◽

Vol 74 (6) ◽

pp. 1288-1310 ◽

Author(s):

Raimund Bürger ◽

Sudarshan Kumar Kenettinkara ◽

David Zorío

Keyword(s):

Conservation Laws ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Hyperbolic Conservation Laws ◽

Galerkin Methods ◽

Hyperbolic Conservation

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Implicit time integration of hyperbolic conservation laws via discontinuous Galerkin methods

International Journal for Numerical Methods in Biomedical Engineering ◽

10.1002/cnm.1326 ◽

2011 ◽

Vol 27 (5) ◽

pp. 711-721 ◽

Author(s):

J. Xin ◽

J. E. Flaherty

Keyword(s):

Conservation Laws ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Hyperbolic Conservation Laws ◽

Time Integration ◽

Implicit Time ◽

Galerkin Methods ◽

Hyperbolic Conservation ◽

Implicit Time Integration

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hp-Version discontinuous Galerkin methods for hyperbolic conservation laws

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/0045-7825(95)00944-2 ◽

1996 ◽

Vol 133 (3-4) ◽

pp. 259-286 ◽

Author(s):

Kim S. Bey ◽

J. Tinsley Oden

Keyword(s):

Conservation Laws ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Hyperbolic Conservation Laws ◽

Galerkin Methods ◽

Hyperbolic Conservation

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