Discontinuous Galerkin Methods for Variational Inequalities and PDE-Constrained Optimizations

Abstract: Variational inequalities and PDE-Constrained optimization appear in many applications and have recently received a significant attention. In this talk, we will first study a family of discontinuous Galerkin methods for solving a fourth order obstacle problem which represents the variational inequality of the first kind. Then we focus on an elliptic state-constrained optimal control problem and propose a novel finite element method to solve it. Both a priori and a posteriori analysis will be discussed. We will also present numerical results to gauge the performance of the proposed methods.