International Journal of Mathematics and Mathematical Sciences 
Volume 27 (2001), Issue 5, Pages 309-319
doi:10.1155/S0161171201010602

L∞-error estimates for a class of semilinear elliptic variational inequalities and quasi-variational inequalities

M. Boulbrachene,1 P. Cortey-Dumont,2 and J. C. Miellou3

 1Department of Mathematics and Statistics, Sultan Qaboos University, P.O. Box 36, Muscat 123, Oman
2Departement de Marketing Scientifique, IBM, Tour Septentrion, La Défense, 92800 Puteaux, Paris, France
3Laboratoire de Calcul Scientifique, 16 Route de Gray, 25030 Besancon Cedex France, Paris, France
Received 30 July 2000

Abstract

This paper deals with the finite element approximation of a class of variational inequalities (VI) and quasi-variational inequalities (QVI) with the right-hand side depending upon the solution. We prove that the approximation is optimally accurate in L∞ combining the Banach fixed point theorem with the standard uniform error estimates in linear VIs and QVIs. We also prove that this approach extends successfully to the corresponding noncoercive problems.