Implicit Positivity-Preserving High-Order Discontinuous Galerkin Methods for Conservation Laws

SIAM Journal on Scientific Computing ◽

10.1137/17m112436x ◽

2018 ◽

Vol 40 (1) ◽

pp. A81-A107 ◽

Author(s):

Tong Qin ◽

Chi-Wang Shu

Keyword(s):

Conservation Laws ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Positivity Preserving

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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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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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An entropy-residual shock detector for solving conservation laws using high-order discontinuous Galerkin methods

Journal of Computational Physics ◽

10.1016/j.jcp.2016.06.052 ◽

2016 ◽

Vol 322 ◽

pp. 448-472 ◽

Author(s):

Yu Lv ◽

Yee Chee See ◽

Matthias Ihme

Keyword(s):

Conservation Laws ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods

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High Order Positivity-Preserving Discontinuous Galerkin Methods for Radiative Transfer Equations

SIAM Journal on Scientific Computing ◽

10.1137/16m1061072 ◽

2016 ◽

Vol 38 (5) ◽

pp. A2987-A3019 ◽

Author(s):

Daming Yuan ◽

Juan Cheng ◽

Chi-Wang Shu

Keyword(s):

Radiative Transfer ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Positivity Preserving ◽

Transfer Equations ◽

Radiative Transfer Equations

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Positivity-preserving high order well-balanced discontinuous Galerkin methods for the shallow water equations

Advances in Water Resources ◽

10.1016/j.advwatres.2010.08.005 ◽

2010 ◽

Vol 33 (12) ◽

pp. 1476-1493 ◽

Author(s):

Yulong Xing ◽

Xiangxiong Zhang ◽

Chi-Wang Shu

Keyword(s):

Shallow Water ◽

Discontinuous Galerkin ◽

Shallow Water Equations ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Positivity Preserving

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Conservative High Order Positivity-Preserving Discontinuous Galerkin Methods for Linear Hyperbolic and Radiative Transfer Equations

Journal of Scientific Computing ◽

10.1007/s10915-018-0700-3 ◽

2018 ◽

Vol 77 (3) ◽

pp. 1801-1831 ◽

Author(s):

Dan Ling ◽

Juan Cheng ◽

Chi-Wang Shu

Keyword(s):

Radiative Transfer ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Positivity Preserving ◽

Transfer Equations ◽

Radiative Transfer Equations

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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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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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Positivity-Preserving Well-Balanced Arbitrary Lagrangian–Eulerian Discontinuous Galerkin Methods for the Shallow Water Equations

Journal of Scientific Computing ◽

10.1007/s10915-021-01578-w ◽

2021 ◽

Vol 88 (3) ◽

Author(s):

Weijie Zhang ◽

Yinhua Xia ◽

Yan Xu

Keyword(s):

Shallow Water ◽

Discontinuous Galerkin ◽

Shallow Water Equations ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Arbitrary Lagrangian Eulerian ◽

Positivity Preserving

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Efficient High Order Semi-implicit Time Discretization and Local Discontinuous Galerkin Methods for Highly Nonlinear PDEs

Journal of Scientific Computing ◽

10.1007/s10915-016-0170-4 ◽

2016 ◽

Vol 68 (3) ◽

pp. 1029-1054 ◽

Author(s):

Ruihan Guo ◽

Francis Filbet ◽

Yan Xu

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Time Discretization ◽

Nonlinear Pdes ◽

Implicit Time ◽

Galerkin Methods ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods ◽

Highly Nonlinear

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