The finite element approximation in parabolic quasi-variational inequalities related to impulse control problem with mixed boundary conditions

This paper is an extension for our previous results [3], [4] and [5], and it deals with the finite element approximation of a parabolic quasi-variational inequalities with mixed boundary conditions. A quasi-optimal L∞-error estimate is established using a new discrete algorithm stands in theta time scheme combined with a finite element spatial approximation. Our approach stands on a discrete L∞-stability property with respect to the right-hand side where the obstacle defined as an impulse control problem.