Local Discontinuous Galerkin Methods for the abcd Nonlinear Boussinesq System

被引：0
作者：
Jiawei Sun
Shusen Xie
Yulong Xing
机构：
[1] The Ohio State University,Department of Mathematics
[2] Ocean University of China,School of Mathematical Sciences
来源：
Communications on Applied Mathematics and Computation | 2022年 / 4卷
关键词：
Local discontinuous Galerkin methods; Boussinesq equations; Coupled BBM equations; Error estimate; Numerical fluxes; Head-on collision; 65M12; 65M15; 65M60;
D O I：
暂无
中图分类号：
学科分类号：
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.
引用
收藏
页码：381 / 416
页数：35
相关论文
共 61 条
  • [21] Mitsotakis DE(2020)Optimal energy conserving and energy dissipative local discontinuous Galerkin methods for the Benjamin-Bona-Mahony equation Journal of Computational Physics 401 109002-330
  • [22] Boussinesq J(2015)Energy conserving local discontinuous Galerkin methods for the improved Boussinesq equation ESAIM: M2AN 49 991-3822
  • [23] Buli J(1966)A priori error estimates to smooth solutions of the third order Runge-Kutta discontinuous Galerkin method for symmetrizable systems of conservation laws J. Fluid Mech. 25 321-46
  • [24] Xing Y(2007)Calculations of the development of an undular bore Comput. Methods Appl. Mech. Eng. 196 3805-104
  • [25] Burtea C(2010)Error estimates of the semi-discrete local discontinuous Galerkin method for nonlinear convection-diffusion and KdV equations Commun. Comput. Phys. 7 1-undefined
  • [26] Courtès C(2012)Local discontinuous Galerkin methods for high-order time-dependent partial differential equations SIAM J. Numer. Anal. 50 79-undefined
  • [27] Chen M(undefined)Optimal error estimates of the semi-discrete local discontinuous Galerkin methods for high order wave equations undefined undefined undefined-undefined
  • [28] Cockburn B(undefined)undefined undefined undefined undefined-undefined
  • [29] Hou S(undefined)undefined undefined undefined undefined-undefined
  • [30] Shu C-W(undefined)undefined undefined undefined undefined-undefined
1234567