J. Comp. Math., 33 (2015), pp. 307-322.


A Modified Weak Galerkin Finite Element Method for Sobolev Equation

Fuzheng Gao 1, Xiaoshen Wang 2

1 School of Mathematics, Shandong University, Jinan, Shandong 250100, China; School of Materials Science and Engineering, Shandong University, Jinan, Shandong, China
2 Department of Mathematics, University of Arkansas at Little Rock, 2801 S. University Avenue, Little Rock, AR 72204, USA

Received 2014-4-10 Accepted 2015-2-4
Available online 2015-5-15
doi:10.4208/jcm.1502-m4509

Abstract

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 H¹ and L² norms are established for the corresponding modified weak Galerkin finite element solutions. Finally, some numerical results are given to verify theoretical results.

Key words: Galerkin FEMs, Sobolev equation, Discrete weak gradient, Modified weak Galerkin, Error estimate.

AMS subject classifications: 65M15, 65M60.


Email: fzgao@sdu.edu.cn, xxwang@ualr.edu
 

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