International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 24, Pages 1547-1561
doi:10.1155/S016117120301189X

L∞-error estimate for a system of elliptic quasivariational inequalities

M. Boulbrachene,1 M. Haiour,2 and S. Saadi2,3

1Department of Mathematics and Statistics, College of Science, Sultan Qaboos University, P.O. Box 36, Al-Khad, 123, Oman
2Département de Mathématiques, Faculté des Sciences, Université de Annaba, BP 12, Annaba 23000, Algeria
3The Abdus Salam International Centre for Theoretical Physics, Mathematics Section, P.O. Box 586, Trieste I 34100, Italy

Received 6 February 2001; Revised 22 October 2001

Copyright © 2003 M. Boulbrachene 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

We deal with the numerical analysis of a system of elliptic quasivariational inequalities (QVIs). Under W2,p(Ω)-regularity of the continuous solution, a quasi-optimal L∞-convergence of a piecewise linear finite element method is established, involving a monotone algorithm of Bensoussan-Lions type and standard uniform error estimates known for elliptic variational inequalities (VIs).