Abstract
In this paper, the parabolic quasi-variational inequalities are transformed into a noncoercive elliptic quasi-variational inequalities. A new iterative discrete algorithm is proposed to show the existence and uniqueness, and a simple proof to asymptotic behavior in uniform norm is also given using the theta time scheme combined with a finite element spatial approximation. The proposed approach stands on a discrete L-infinity-stability property with respect to the right-hand side and obstacle defined as an impulse control problem. (C) 2011 Elsevier Inc. All rights reserved.