CONVERGENCE ANALYSIS OF A DISCONTINUOUS GALERKIN METHOD FOR WAVE EQUATIONS IN SECOND-ORDER FORM

被引：2

作者：

Du, Yu ^{[1
,2
]}

Zhang, Lu ^{[3
]}

Zhang, Zhimin ^{[1
,4
]}

机构：

[1] Beijing Computat Sci Res Ctr, Beijing 100193, Peoples R China

[2] Xiangtan Univ, Sch Math & Computat Sci, Xiangtan 411105, Peoples R China

[3] Southern Methodist Univ, Dept Math, Dallas, TX 75205 USA

[4] Wayne State Univ, Dept Math, Detroit, MI 48202 USA

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2019年 / 57卷 / 01期

基金：

中国国家自然科学基金; 美国国家科学基金会;

关键词：

discontinuous Galerkin method; wave equation; supercloseness; superconvergence; PPR; POLYNOMIAL PRESERVING RECOVERY; HELMHOLTZ-EQUATION; GRADIENT RECOVERY; SUPERCONVERGENCE; DISCRETIZATIONS;

D O I：

10.1137/18M1190495

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study the convergence property of a spatial discontinuous Galerkin method for wave equations. We prove an optimal convergence rate in the energy norm, which improves an existing suboptimal a priori error estimate. In addition, by adding a penalty term to the variational form, we obtain a supercloseness result, based on which we prove superconvergence of a postprocessed gradient, where the postprocessing operator is the polynomial preserving recovery. All theoretical findings are verified by numerical tests.

引用

页码：238 / 265

页数：28

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