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

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).