L2-error analysis of discontinuous Galerkin approximations for nonlinear Sobolev equations

被引：6

作者：

Ohm, Mi Ray ^{[1
]}

Lee, Hyun Young ^{[2
]}

Shin, Jun Yong ^{[3
]}

机构：

[1] Dongseo Univ, Div Informat Syst Engn, Pusan 617716, South Korea

[2] Kyungsung Univ, Dept Math, Pusan 608736, South Korea

[3] Pukyong Natl Univ, Dept Appl Math, Pusan 608737, South Korea

来源：

JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS | 2013年 / 30卷 / 01期

关键词：

Nonlinear Sobolev equations; L-2-error estimation; Discontinuous Galerkin approximations; Symmetric interior penaltymethod; FINITE-ELEMENT METHODS;

D O I：

10.1007/s13160-012-0096-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We apply a discontinuous Galerkin method with symmetric interior penalty terms to approximate the solution of nonlinear Sobolev equations. And we introduce an appropriate elliptic type projection of the solution of a Sobolev equation and prove its optimal convergence. Finally we construct semidiscrete approximations of the solutions of nonlinear Sobolev differential equations, and prove that they converge in L-2 normed space with optimal order of convergence.

引用

页码：91 / 110

页数：20

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