Hamburger Beiträge zur Angewandten Mathematik A Posteriori Error Representations for Elliptic Optimal Control Problems with Control and State Constraints

In this work we develop an adaptive algorithm for solving elliptic optimal control problems with simultaneously appearing state and control constraints. Building upon the concept proposed in [9] the algorithm applies a Moreau-Yosida regularization technique for handling state constraints. The state and co-state variables are discretized using continuous piecewise linear finite elements while a variational discretization concept is applied for the control. To perform the adaptive mesh refinement cycle we derive local error representations which extend the goal-oriented error approach to our setting. The performance of the overall adaptive solver is demonstrated by a numerical example. Mathematics Subject Classification (2000). 49J20; 65N30; 65N50.