On the finite element approximation of elliptic QVIs with noncoercive operators

In this paper, we extend the approach developed by the author for the standard finite element method in the L^∞-norm of the noncoercive variational inequalities (VI) (Numer Funct Anal Optim.2015;36:1107-1121.) to impulse control quasi-variational inequality (QVI). We derive the optimal error estimate, combining the so-called Bensoussan-Lions Algorithm and the concept of subsolutions for VIs.