Optimal error estimate for a system of several quasi variational inequalities

This paper presents and examines a finite element approximation for a system of multiple quasi-variational inequalities. We analyze these inequalities, including terms for sources and obstacles that depend on the solution itself. An optimal $L^{\infty}$ -error estimate is derived by combining a modified Bensoussan-Lions type algorithm with established uniform error estimates for elliptic variational inequalities (VI).