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

Andreas Dedner; Charalambos Makridakis; Mario Ohlberger

doi:10.1137/050624248

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 ◽

Cited By ~ 20

Author(s):

Andreas Dedner ◽

Charalambos Makridakis ◽

Mario Ohlberger

Keyword(s):

Conservation Laws ◽

Discontinuous Galerkin ◽

Error Control ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Nonlinear Conservation Laws ◽

Runge Kutta

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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 ◽

Cited By ~ 39

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

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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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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 ◽

Entropy Stable

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Runge-Kutta and Lax-Wendroff discontinuous Galerkin methods for linear conservation laws

10.1063/1.4992491 ◽

2017 ◽

Cited By ~ 1

Author(s):

Chi-Wang Shu

Keyword(s):

Conservation Laws ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Runge Kutta

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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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WEIGHTED NON-OSCILLATORY LIMITERS FOR RUNGE-KUTTA DISCONTINUOUS GALERKIN METHODS

Advances in Computational Fluid Dynamics - Adaptive High-Order Methods in Computational Fluid Dynamics ◽

10.1142/9789814313193_0006 ◽

2011 ◽

pp. 153-184

Author(s):

Jianxian Qiu

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Runge Kutta

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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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Adaptive Runge-Kutta Discontinuous Galerkin Methods with Modified Ghost Fluid Method for Simulating the Compressible Two-Medium Flow

Journal of Mathematical Study ◽

10.4208/jms.v47n3.14.02 ◽

2014 ◽

Vol 47 (3) ◽

pp. 250-273 ◽

Cited By ~ 1

Author(s):

J. Zhu and J. Qiu

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Ghost Fluid Method ◽

Medium Flow ◽

Runge Kutta ◽

Modified Ghost Fluid Method

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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 ◽

Cited By ~ 4

Author(s):

Mi-Young Kim ◽

Eun-Jae Park ◽

Jaemin Shin

Keyword(s):

Conservation Laws ◽

Discontinuous Galerkin ◽

Lagrange Multiplier ◽

Discontinuous Galerkin Methods ◽

Hyperbolic Systems ◽

High Order ◽

Galerkin Methods ◽

Systems Of Conservation Laws

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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 ◽

Cited By ~ 44

Author(s):

Bernardo Cockburn

Keyword(s):

Conservation Laws ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Hyperbolic Conservation Laws ◽

Galerkin Methods ◽

Hyperbolic Conservation ◽

Non Linear

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