L∞ Error Estimate for the Noncoercive Impulse Control QVI: A New Approach

Abstract

In this paper, we introduce a new method to analyze the convergence of the standard finite element method for the noncoercive impulse control quasi-variational inequality (QVI). L^∞ convergence of the approximation is derived as a result of the geometrical convergence of a Bensoussan–Lions algorithm type and uniform error estimate between the continuous algorithm and its finite element counterpart. This approach is completely different from the one inroduced in [2] as it enables us to derive the error estimate through a computational iterative scheme.