A Problem-Independent Limiter for High-Order Runge–Kutta Discontinuous Galerkin Methods

A. Burbeau; P. Sagaut; Ch.-H. Bruneau

doi:10.1006/jcph.2001.6718

A Problem-Independent Limiter for High-Order Runge–Kutta Discontinuous Galerkin Methods

Journal of Computational Physics ◽

10.1006/jcph.2001.6718 ◽

2001 ◽

Vol 169 (1) ◽

pp. 111-150 ◽

Cited By ~ 145

Author(s):

A. Burbeau ◽

P. Sagaut ◽

Ch.-H. Bruneau

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

High Order ◽

Galerkin Methods ◽

Runge Kutta

Download Full-text

High-order Runge-Kutta discontinuous Galerkin methods with a new type of multi-resolution WENO limiters on triangular meshes

Applied Numerical Mathematics ◽

10.1016/j.apnum.2020.03.013 ◽

2020 ◽

Vol 153 ◽

pp. 519-539

Author(s):

Jun Zhu ◽

Chi-Wang Shu ◽

Jianxian Qiu

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

High Order ◽

Galerkin Methods ◽

Triangular Meshes ◽

New Type ◽

Runge Kutta

Download Full-text

High order sign-preserving and well-balanced exponential Runge-Kutta discontinuous Galerkin methods for the shallow water equations with friction

Journal of Computational Physics ◽

10.1016/j.jcp.2021.110543 ◽

2021 ◽

pp. 110543

Author(s):

Ruize Yang ◽

Yang Yang ◽

Yulong Xing

Keyword(s):

Shallow Water ◽

Discontinuous Galerkin ◽

Shallow Water Equations ◽

Discontinuous Galerkin Methods ◽

High Order ◽

Galerkin Methods ◽

Runge Kutta

Download Full-text

High-order Runge-Kutta discontinuous Galerkin methods with multi-resolution WENO limiters for solving steady-state problems

Applied Numerical Mathematics ◽

10.1016/j.apnum.2021.03.011 ◽

2021 ◽

Vol 165 ◽

pp. 482-499

Author(s):

Jun Zhu ◽

Chi-Wang Shu ◽

Jianxian Qiu

Keyword(s):

Steady State ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

High Order ◽

Galerkin Methods ◽

Runge Kutta

Download Full-text

High-Order Runge-Kutta Discontinuous Galerkin Methods with a New Type of Multi-Resolution WENO Limiters on Tetrahedral Meshes

Communications in Computational Physics ◽

10.4208/cicp.oa-2020-0096 ◽

2021 ◽

Vol 29 (4) ◽

pp. 1030-1058

Author(s):

Jun Zhu

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

High Order ◽

Galerkin Methods ◽

Tetrahedral Meshes ◽

New Type ◽

Runge Kutta

Download Full-text

High-order Runge-Kutta discontinuous Galerkin methods with a new type of multi-resolution WENO limiters

Journal of Computational Physics ◽

10.1016/j.jcp.2019.109105 ◽

2020 ◽

Vol 404 ◽

pp. 109105 ◽

Cited By ~ 5

Author(s):

Jun Zhu ◽

Jianxian Qiu ◽

Chi-Wang Shu

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

High Order ◽

Galerkin Methods ◽

New Type ◽

Runge Kutta

Download Full-text

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 ◽

Cited By ~ 7

Author(s):

Ruihan Guo ◽

Francis Filbet ◽

Yan Xu

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Time Discretization ◽

High Order ◽

Nonlinear Pdes ◽

Implicit Time ◽

Galerkin Methods ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods ◽

Highly Nonlinear

Download Full-text

Comparison of high order finite element and discontinuous Galerkin methods for phase field equations: Application to structural damage

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2017.05.003 ◽

2017 ◽

Vol 74 (7) ◽

pp. 1542-1564 ◽

Cited By ~ 2

Author(s):

L.R. Chiarelli ◽

F.G. Fumes ◽

E.A. Barros de Moraes ◽

G.A. Haveroth ◽

J.L. Boldrini ◽

...

Keyword(s):

Finite Element ◽

Discontinuous Galerkin ◽

Phase Field ◽

Structural Damage ◽

Discontinuous Galerkin Methods ◽

High Order ◽

Galerkin Methods ◽

Field Equations ◽

Phase Field Equations

Download Full-text

High-Order Mesh Generation for Discontinuous Galerkin Methods Based on Elastic Deformation

Advances in Applied Mathematics and Mechanics ◽

10.4208/aamm.2014.m618 ◽

2016 ◽

Vol 8 (4) ◽

pp. 693-702

Author(s):

Hongqiang Lu ◽

Kai Cao ◽

Lechao Bian ◽

Yizhao Wu

Keyword(s):

Finite Element Method ◽

Discontinuous Galerkin ◽

Mesh Generation ◽

Discontinuous Galerkin Methods ◽

Elasticity Modulus ◽

High Order ◽

Galerkin Methods ◽

Governing Equations ◽

Numerical Tests ◽

Cubic Polynomial

AbstractIn this paper, a high-order curved mesh generation method for Discontinuous Galerkin methods is introduced. First, a regular mesh is generated. Second, the solid surface is re-constructed using cubic polynomial. Third, the elastic governing equations are solved using high-order finite element method to provide a fully or partly curved grid. Numerical tests indicate that the intersection between element boundaries can be avoided by carefully defining the elasticity modulus.

Download Full-text