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

In this paper, we present the uniform framework of local discontinuous Galerkin (LDG) methods for two-dimensional Camassa–Holmequations and two-dimensional μ-Camassa–Holmequations. The energy stability and the semi-discrete error estimates based on the uniform framework for two equations are derived...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2023-03, Vol.420, p.114722, Article 114722
Main Authors: Lu, Jinyang, Xu, Yan, Zhang, Chao
Format: Article
Language:English
Subjects:
Error estimates
Local discontinuous Galerkin method
Two-dimensional [formula omitted]-Camassa–Holm equation
Two-dimensional Camassa–Holm equation
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Summary:In this paper, we present the uniform framework of local discontinuous Galerkin (LDG) methods for two-dimensional Camassa–Holmequations and two-dimensional μ-Camassa–Holmequations. 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.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2022.114722