Local Discontinuous Galerkin Methods for the abcd Nonlinear Boussinesq System

doi:10.1007/s42967-021-00119-4

Communications on Applied Mathematics and Computation ›› 2022, Vol. 4 ›› Issue (2): 381-416.doi: 10.1007/s42967-021-00119-4

• ORIGINAL PAPERS • 下一篇

Local Discontinuous Galerkin Methods for the abcd Nonlinear Boussinesq System

Jiawei Sun¹, Shusen Xie², Yulong Xing¹

1 Department of Mathematics, The Ohio State University, Columbus, OH 43210, USA;
2 School of Mathematical Sciences, Ocean University of China, Qingdao 266100, Shandong, China

收稿日期:2020-08-30 修回日期:2020-11-30 出版日期:2022-06-20 发布日期:2022-04-29
通讯作者: Jiawei Sun, Shusen Xie, Yulong Xing E-mail:xing.205@osu.edu;sun.2261@buckeyemail.osu.edu;shusenxie@ouc.edu.cn
基金资助:
The work of J. Sun and Y. Xing is partially sponsored by NSF grant DMS-1753581.

Local Discontinuous Galerkin Methods for the abcd Nonlinear Boussinesq System

Jiawei Sun¹, Shusen Xie², Yulong Xing¹

1 Department of Mathematics, The Ohio State University, Columbus, OH 43210, USA;
2 School of Mathematical Sciences, Ocean University of China, Qingdao 266100, Shandong, China

Received:2020-08-30 Revised:2020-11-30 Online:2022-06-20 Published:2022-04-29
Contact: Jiawei Sun, Shusen Xie, Yulong Xing E-mail:xing.205@osu.edu;sun.2261@buckeyemail.osu.edu;shusenxie@ouc.edu.cn
Supported by:
The work of J. Sun and Y. Xing is partially sponsored by NSF grant DMS-1753581.

摘要/Abstract

摘要： Boussinesq type equations have been widely studied to model the surface water wave. In this paper, we consider the abcd Boussinesq system which is a family of Boussinesq type equations including many well-known models such as the classical Boussinesq system, the BBM-BBM system, the Bona-Smith system, etc. We propose local discontinuous Galerkin (LDG) methods, with carefully chosen numerical fluxes, to numerically solve this abcd Boussinesq system. The main focus of this paper is to rigorously establish a priori error estimate of the proposed LDG methods for a wide range of the parameters a, b, c, d. Numerical experiments are shown to test the convergence rates, and to demonstrate that the proposed methods can simulate the head-on collision of traveling wave and finite time blow-up behavior well.

关键词: Local discontinuous Galerkin methods, Boussinesq equations, Coupled BBM equations, Error estimate, Numerical fluxes, Head-on collision

Abstract: Boussinesq type equations have been widely studied to model the surface water wave. In this paper, we consider the abcd Boussinesq system which is a family of Boussinesq type equations including many well-known models such as the classical Boussinesq system, the BBM-BBM system, the Bona-Smith system, etc. We propose local discontinuous Galerkin (LDG) methods, with carefully chosen numerical fluxes, to numerically solve this abcd Boussinesq system. The main focus of this paper is to rigorously establish a priori error estimate of the proposed LDG methods for a wide range of the parameters a, b, c, d. Numerical experiments are shown to test the convergence rates, and to demonstrate that the proposed methods can simulate the head-on collision of traveling wave and finite time blow-up behavior well.

Key words: Local discontinuous Galerkin methods, Boussinesq equations, Coupled BBM equations, Error estimate, Numerical fluxes, Head-on collision

中图分类号:

Jiawei Sun, Shusen Xie, Yulong Xing. Local Discontinuous Galerkin Methods for the abcd Nonlinear Boussinesq System[J]. Communications on Applied Mathematics and Computation, 2022, 4(2): 381-416.

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Local Discontinuous Galerkin Methods for the abcd Nonlinear Boussinesq System

Local Discontinuous Galerkin Methods for the abcd Nonlinear Boussinesq System

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