A MODIFIED WEAK GALERKIN FINITE ELEMENT METHOD FOR SOBOLEV EQUATION

For Sobolev equation, we present a new numerical scheme based on a modified weak Galerkin finite element method, in which differential operators are approximated by weak forms through the usual integration by parts. In particular, the numerical method allows the use of discontinuous finite element f...

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Bibliographic Details
Published inJournal of computational mathematics Vol. 33; no. 3; pp. 307 - 322
Main Authors Gao, Fuzheng, Wang, Xiaoshen
Format Journal Article
LanguageEnglish
Published Chinese Academy of Mathematices and System Sciences (AMSS) Chinese Academy of Sciences 01.05.2015
Subjects
Galerkin有限元法
Sobolev方程
任意形状
微分算子
数值方法
最优误差估计
索伯列夫方程
间断有限元
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ISSN0254-9409
1991-7139
DOI10.4208/jcm.1502-m4509

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Summary:For Sobolev equation, we present a new numerical scheme based on a modified weak Galerkin finite element method, in which differential operators are approximated by weak forms through the usual integration by parts. In particular, the numerical method allows the use of discontinuous finite element functions and arbitrary shape of element. Optimal order error estimates in discrete H^1 and L^2 norms are established for the corresponding modified weak Galerkin finite element solutions. Finally, some numerical results are given to verify theoretical results.
Bibliography:11-2126/O1
Galerkin FEMs, Sobolev equation, Discrete weak gradient, Modified weak Galerkin, Error estimate
For Sobolev equation, we present a new numerical scheme based on a modified weak Galerkin finite element method, in which differential operators are approximated by weak forms through the usual integration by parts. In particular, the numerical method allows the use of discontinuous finite element functions and arbitrary shape of element. Optimal order error estimates in discrete H^1 and L^2 norms are established for the corresponding modified weak Galerkin finite element solutions. Finally, some numerical results are given to verify theoretical results.
ISSN:0254-9409
1991-7139
DOI:10.4208/jcm.1502-m4509