A posteriori error estimates for adaptive finite element discretizations of boundary control problems

Abstract

We are concerned with an a posteriori error analysis of adaptive finite element approximations of boundary control problems for second order elliptic boundary value problems under bilateral bound constraints on the control which acts through a Neumann type boundary condition. In particular, the analysis of the errors in the state, the co-state, the control, and the co-control invokes an efficient and reliable residual-type a posteriori error estimator as well as data oscillations. The proof of the efficiency and reliability is done without any regularity assumption. Adaptive mesh refinement is realized on the basis of a bulk criterion. The performance of the adaptive finite element approximation is illustrated by a detailed documentation of numerical results for selected test problems.