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A well-balanced element-free Galerkin method for the nonlinear shallow water equations

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  • Yuan, Xu-hua

Abstract

In this paper, we consider the nonlinear shallow water equations over variable bottom topography in one dimension and propose a well-balanced element-free Galerkin method for solving this system. The proposed scheme has the features of being high-order accurate for general solutions and exactly preserving the still-water stationary solution. The main ingredient to achieve the well-balanced property is to use a special decomposition to the source term and discretize the source term as the flux term. Numerical tests are presented to illustrate the accuracy and validity of the proposed scheme.

Suggested Citation

  • Yuan, Xu-hua, 2018. "A well-balanced element-free Galerkin method for the nonlinear shallow water equations," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 46-53.
    • Handle: RePEc:eee:apmaco:v:331:y:2018:i:c:p:46-53
    DOI: 10.1016/j.amc.2018.01.061
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    Cited by:

    1. Zhizhuang Zhang & Xiangyu Zhou & Gang Li & Shouguo Qian & Qiang Niu, 2023. "A New Entropy Stable Finite Difference Scheme for Hyperbolic Systems of Conservation Laws," Mathematics, MDPI, vol. 11(12), pages 1-18, June.
    2. Li, Gang & Li, Jiaojiao & Qian, Shouguo & Gao, Jinmei, 2021. "A well-balanced ADER discontinuous Galerkin method based on differential transformation procedure for shallow water equations," Applied Mathematics and Computation, Elsevier, vol. 395(C).

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