A posteriori error control of a state constrained elliptic control problem

Abstract

We develop an adaptive finite element concept for elliptic optimal control problems with constraints on the state. In order to generate goal-oriented meshes, we extend the Dual Weighted Residual (DWR) concept proposed by Becker and Rannacher for PDE-constrained optimization to the state constrained case. Using the optimality system of the underlying PDE-constrained optimal control problem we obtain a representation for the error in the objectives. Based on this representation we define local error indicators, whose performance we investigate by means of a numerical example.