Goal-Oriented Adaptivity in Control Constrained Optimal Control of Partial Differential Equations

Abstract

Dual-weighted goal-oriented error estimates for a class of pointwise control constrained optimal control problems for second order elliptic partial differential equations are derived. It is demonstrated that the constraints give rise to a primal-dual weighted error term representing the mismatch in the complementarity system due to discretization. The paper also contains a posteriori error estimators for the $L^2$-norm of the error in the state and in the adjoint state.