Error estimates of the local discontinuous Galerkin methods for two-dimensional (μ)-Camassa-Holm equations

被引：1

作者：

Lu, Jinyang ^{[1
]}

Xu, Yan ^{[1
]}

Zhang, Chao ^{[1
]}

机构：

[1] Univ Sci & Technol China, Sch Math Sci, Hefei 230026, Anhui, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2023年 / 420卷

关键词：

Two-dimensional Camassa-Holm equation; Two-dimensional mu-Camassa-Holm equation; Error estimates; Local discontinuous Galerkin method; FINITE-ELEMENT-METHOD; KORTEWEG-DE-VRIES; CAMASSA-HOLM; CONSERVATION-LAWS; PROJECTION; CONVECTION; DIFFUSION; CONVERGENCE; SCHEME;

D O I：

10.1016/j.cam.2022.114722

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we present the uniform framework of local discontinuous Galerkin (LDG) methods for two-dimensional Camassa-Holm equations and two-dimensional mu-Camassa-Holm equations. The energy stability and the semi-discrete error estimates based on the uniform framework for two equations are derived. The optimal error estimates with order k for approximating the first-order derivatives with Qk elements in Cartesian meshes are obtained. Compared with the error estimates for one-dimensional cases, more auxiliary variables and inter-element jump terms make the derivation more complicated. Numerical experiments for different circumstances are displayed to illustrate the accuracy and stability of those schemes. (c) 2022 Elsevier B.V. All rights reserved.

引用

页数：29

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