Discontinuous Galerkin Methods for an Elliptic Optimal Control Problem with a General State Equation and Pointwise State Constraints

We investigate discontinuous Galerkin methods for an elliptic optimal control problem with a general state equation and pointwise state constraints on general polygonal domains. We show that discontinuous Galerkin methods for general second-order elliptic boundary value problems can be used to solve the elliptic optimal control problems with pointwise state constraints. We establish concrete error estimates and numerical experiments are shown to support the theoretical results.