On the finite element approximation of elliptic QVIs with noncoercive operators

Abstract

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.

OptimalL∞‐error estimate for the semilinear impulse control quasi‐variational inequality

“…On the numerical analysis side and more specifically their finite element approximation in the maximum norm, a good amount of work has been achieved for linear QVIs (cf., e.g., previous studies [3][4][5][6][7] ), where various and different methods were employed.…”