Journal of Applied Mathematics
Volume 2012 (2012), Article ID 156095, 12 pages
http://dx.doi.org/10.1155/2012/156095
Research Article

Superconvergence Analysis of Finite Element Method for a Second-Type Variational Inequality

Dongyang Shi,1 Hongbo Guan,1,2 and Xiaofei Guan3

1Department of Mathematics, Zhengzhou University, Zhengzhou 450001, China
2Department of Mathematics and Information Science, Zhengzhou University of Light Industry, Zhengzhou 450002, China
3Department of Mathematics, Tongji University, Shanghai 200092, China

Received 10 May 2012; Accepted 14 October 2012

Academic Editor: Song Cen

Copyright © 2012 Dongyang Shi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper studies the finite element (FE) approximation to a second-type variational inequality. The supe rclose and superconvergence results are obtained for conforming bilinear FE and nonconforming FE schemes under a reasonable regularity of the exact solution , which seem to be never discovered in the previous literature. The optimal -norm error estimate is also derived for FE. At last, some numerical results are provided to verify the theoretical analysis.