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

被引：11

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.

引用

页数：16

共 50 条

[41] A two-grid method for discontinuous Galerkin approximations to nonlinear Sobolev equations [J].

Yang, Jiming ;

Zhou, Jing .

NUMERICAL ALGORITHMS, 2021, 86 (04) :1523-1541

[42] An effective discontinuous Galerkin method for solving acoustic wave equations in heterogeneous media [J].

He, Xijun ;

Wang, Qiyue ;

Zhou, Yanjie ;

Huang, Jiandong ;

Huang, Xueyuan .

JOURNAL OF GEOPHYSICS AND ENGINEERING, 2025, 22 (01) :105-118

[43] AN ENERGY-BASED DISCONTINUOUS GALERKIN METHOD FOR THE NONLINEAR SCHRO"\DINGER EQUATION WITH WAVE OPERATOR [J].

Ren, Kui ;

Zhang, Lu ;

Zhou, Yin .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2024, 62 (06) :2459-2483

[44] Error estimates and post-processing of local discontinuous Galerkin method for Schrodinger equations [J].

Tao, Qi ;

Xia, Yinhua .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2019, 356 :198-218

[45] An Energy Conserving Local Discontinuous Galerkin Method for a Nonlinear Variational Wave Equation [J].

Yi, Nianyu ;

Liu, Hailiang .

COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 2018, 23 (03) :747-772

[46] A New Discontinuous Galerkin Method for Parabolic Equations with Discontinuous Coefficient [J].

Zhang, Rongpei ;

Yu, Xijun ;

Cui, Xia ;

Long, Xiaohan ;

Feng, Tao .

NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS, 2013, 6 (02) :325-342

[47] Superconvergence of the discontinuous Galerkin method for nonlinear second-order initial-value problems for ordinary differential equations [J].

Baccouch, Mahboub .

APPLIED NUMERICAL MATHEMATICS, 2017, 115 :160-179

[48] Error estimates of the discontinuous Galerkin method for nonlinear nonstationary convection-diffusion problems [J].

Dolejsí, V ;

Feistauer, M .

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2005, 26 (03) :349-383

[49] Extrapolation discontinuous Galerkin method for ultraparabolic equations [J].

Marcozzi, Michael D. .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2009, 224 (02) :679-687

[50] A mixed discontinuous Galerkin method for the Biot equations [J].

Wen, Jing .

APPLIED NUMERICAL MATHEMATICS, 2025, 212 :283-299

← 1 2 3 4 5 →