A weak Galerkin finite element method for nonlinear conservation laws

Xiu Ye; Shangyou Zhang; Peng Zhu; Xiu Ye; Shangyou Zhang; Peng Zhu

doi:10.3934/era.2020097

Electronic Research Archive

2021, Volume 29, Issue 1: 1897-1923. doi: 10.3934/era.2020097

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A weak Galerkin finite element method for nonlinear conservation laws

Xiu Ye ^{1
,
,},
Shangyou Zhang ^{2
,},
Peng Zhu ^{3
,}

1.
Department of Mathematics, University of Arkansas at Little Rock, Little Rock, AR 72204, USA
2.
Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA
3.
College of Mathematics, Physics and Information Engineering, Jiaxing University, Jiaxing, Zhejiang 314001, China

Received: 01 April 2020 Revised: 01 July 2020 Published: 16 September 2020
Primary: 65N15, 65N30; Secondary: 35J50

A weak Galerkin (WG) finite element method is presented for nonlinear conservation laws. There are two built-in parameters in this WG framework. Different choices of the parameters will lead to different approaches for solving hyperbolic conservation laws. The convergence analysis is obtained for the forward Euler time discrete and the third order explicit TVDRK time discrete WG schemes respectively. The theoretical results are verified by numerical experiments.
- Weak Galerkin,
- finite element methods,
- weak derivative,
- conservation laws
Citation: Xiu Ye, Shangyou Zhang, Peng Zhu. A weak Galerkin finite element method for nonlinear conservation laws[J]. Electronic Research Archive, 2021, 29(1): 1897-1923. doi: 10.3934/era.2020097

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Abstract

A weak Galerkin (WG) finite element method is presented for nonlinear conservation laws. There are two built-in parameters in this WG framework. Different choices of the parameters will lead to different approaches for solving hyperbolic conservation laws. The convergence analysis is obtained for the forward Euler time discrete and the third order explicit TVDRK time discrete WG schemes respectively. The theoretical results are verified by numerical experiments.

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