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Numerical study of a local discontinuous Galerkin method for the two-dimensional nonlinear Benney equation
Leqiang Zou 1, Leilei Wei 2
1. Basic research department, Henan college of industry and information technology, Jiaozuo 454000
2. College of Science, Henan University of Technology, Zhengzhou 450000
*Correspondence author
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Funding: Tian Yuan Special Foundation （No.11426090）
Opened online: 1 April 2015
Accepted by: none
Citation: Leqiang Zou, Leilei Wei.Numerical study of a local discontinuous Galerkin method for the two-dimensional nonlinear Benney equation[OL]. [ 1 April 2015] http://en.paper.edu.cn/en_releasepaper/content/4635769
 
 
In this paper, we develop, analyze and test a local discontinuous Galerkin (LDG) finite element method for solvingthe two-dimensional nonlinear Benney equation. By choosing the numerical fluxes carefully we prove energystability and give an error estimate. Finally numerical example fornonlinear problem shows that the scheme attains the optimal$(k+1)$-th order of accuracy for piecewise $Q^k$ polynomials ofdegree $k$.
Keywords:the Benney equation, Local discontinuous Galerkin method, Stability, Errorestimates.
 
 
 

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