Discontinuous Galerkin Methods for Nonlinear Scalar Conservation Laws: Generalized Local Lax--Friedrichs Numerical Fluxes

SIAM Journal on Numerical Analysis ◽

10.1137/19m1243798 ◽

2020 ◽

Vol 58 (1) ◽

pp. 1-20 ◽

Author(s):

Jia Li ◽

Dazhi Zhang ◽

Xiong Meng ◽

Boying Wu ◽

Qiang Zhang

Keyword(s):

Conservation Laws ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Scalar Conservation Laws ◽

Numerical Fluxes ◽

Scalar Conservation ◽

Nonlinear Scalar Conservation Laws

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Error estimates to smooth solutions of semi-discrete discontinuous Galerkin methods with quadrature rules for scalar conservation laws

Numerical Methods for Partial Differential Equations ◽

10.1002/num.22089 ◽

2016 ◽

Vol 33 (2) ◽

pp. 467-488 ◽

Author(s):

Juntao Huang ◽

Chi-Wang Shu

Keyword(s):

Conservation Laws ◽

Error Estimates ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Quadrature Rules ◽

Galerkin Methods ◽

Smooth Solutions ◽

Scalar Conservation Laws ◽

Scalar Conservation

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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 ◽

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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Local Piecewise Hyperbolic Reconstruction of Numerical Fluxes for Nonlinear Scalar Conservation Laws

SIAM Journal on Scientific Computing ◽

10.1137/0915054 ◽

1994 ◽

Vol 15 (4) ◽

pp. 892-915 ◽

Author(s):

Antonio Marquina

Keyword(s):

Conservation Laws ◽

Scalar Conservation Laws ◽

Numerical Fluxes ◽

Scalar Conservation ◽

Nonlinear Scalar Conservation Laws

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Recovery-Based Error Estimator for the Discontinuous Galerkin Method for Nonlinear Scalar Conservation Laws in One Space Dimension

Journal of Scientific Computing ◽

10.1007/s10915-015-0030-7 ◽

2015 ◽

Vol 66 (2) ◽

pp. 459-476 ◽

Author(s):

Mahboub Baccouch

Keyword(s):

Conservation Laws ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Space Dimension ◽

Error Estimator ◽

Scalar Conservation Laws ◽

Scalar Conservation ◽

Nonlinear Scalar Conservation Laws ◽

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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Arbitrarily Accurate Non-Oscillatory Schemes for Nonlinear Scalar Conservation Laws with Source Terms II

Computational Fluid Dynamics 2002 ◽

10.1007/978-3-642-59334-5_35 ◽

2003 ◽

pp. 247-252 ◽

Author(s):

Yoko Takakura ◽

Eleuterio F. Toro

Keyword(s):

Conservation Laws ◽

Source Terms ◽

Scalar Conservation Laws ◽

Scalar Conservation ◽

Nonlinear Scalar 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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Implicit–Explicit Local Discontinuous Galerkin Methods with Generalized Alternating Numerical Fluxes for Convection–Diffusion Problems

Journal of Scientific Computing ◽

10.1007/s10915-019-01072-4 ◽

2019 ◽

Vol 81 (3) ◽

pp. 2080-2114 ◽

Author(s):

Haijin Wang ◽

Qiang Zhang ◽

Chi-Wang Shu

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Convection Diffusion ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods ◽

Numerical Fluxes ◽

Diffusion Problems

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Genuinely Nonlinear Scalar Conservation Laws

Grundlehren der mathematischen Wissenschaften - Hyberbolic Conservation Laws in Continuum Physics ◽

10.1007/3-540-29089-3_11 ◽

2005 ◽

pp. 301-342

Keyword(s):

Conservation Laws ◽

Scalar Conservation Laws ◽

Scalar Conservation ◽

Nonlinear Scalar Conservation Laws

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Cell-centered discontinuous Galerkin discretizations for two-dimensional scalar conservation laws on unstructured grids and for one-dimensional Lagrangian hydrodynamics

Computers & Fluids ◽

10.1016/j.compfluid.2010.07.018 ◽

2011 ◽

Vol 46 (1) ◽

pp. 498-504 ◽

Author(s):

François Vilar ◽

Pierre-Henri Maire ◽

Rémi Abgrall

Keyword(s):

Conservation Laws ◽

Discontinuous Galerkin ◽

Unstructured Grids ◽

Two Dimensional ◽

Scalar Conservation Laws ◽

One Dimensional ◽

Lagrangian Hydrodynamics ◽

Scalar Conservation

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