A discontinuous Galerkin method and its error estimate for nonlinear fourth-order wave equations

被引：10
|
作者：
Tao, Qi [1 ]
Xu, Yan [1 ]
Shu, Chi-Wang [2 ]
机构：
[1] Univ Sci & Technol China, Sch Math Sci, Hefei 230026, Anhui, Peoples R China
[2] Brown Univ, Div Appl Math, Providence, RI 02912 USA
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2021年 / 386卷
关键词：
Nonlinear fourth-order wave equation; Discontinuous Galerkin method; Energy conserving; Error estimates;
D O I：
10.1016/j.cam.2020.113230
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, an ultra-weak local discontinuous Galerkin (UWLDG) method for a class of nonlinear fourth-order wave equations is designed and analyzed. The UWLDG method is a new DG method designed for solving partial differential equations (PDEs) with high order spatial derivatives. We prove the energy conserving property of our scheme and its optimal error estimates in the L-2-norm for the solution itself as well as for the auxiliary variables approximating the derivatives of the solution. Compatible high order energy conserving time integrators are also proposed. The theoretical results are confirmed by numerical experiments. (C) 2020 Elsevier B.V. All rights reserved.
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页数：16
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