Table of Contents
ISRN Mathematical Analysis
Volume 2011 (2011), Article ID 703670, 15 pages
http://dx.doi.org/10.5402/2011/703670
Research Article

A New Approach to Asymptotic Behavior for a Finite Element Approximation in Parabolic Variational Inequalities

1Hydrometeorological Institute of Formation and Research, Box. 7019, Seddikia, Oran 31000, Algeria
2Department of Mathematics, Faculty of Science, University of Annaba, Box. 12, Annaba 23000, Algeria

Received 30 March 2011; Accepted 13 May 2011

Academic Editors: G. Garcea and S. Zhang

Copyright © 2011 Salah Boulaaras and Mohamed Haiour. 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

The paper deals with the theta time scheme combined with a finite element spatial approximation of parabolic variational inequalities. The parabolic variational inequalities are transformed into noncoercive elliptic variational inequalities. A simple result to time energy behavior is proved, and a new iterative discrete algorithm is proposed to show the existence and uniqueness. Moreover, its convergence is established. Furthermore, a simple proof to asymptotic behavior in uniform norm is given.