A Priori And A Posteriori Error Estimates For Boundary Control

In this paper, we study adaptive finite element discretization schemes for an optimal control problem governed by elliptic PDE with a pointwise constraint for the control, with the constraints set K={u∈L2((?)Ω)u≥β}. We derive the first-order optimality condi-tions from the boundary control problem. Finite element approximations are constructed on different meshes, which are suitable to treat different regularities of the control and state variables. A priori error estimates of optimal control for the finite element approximations are obtained. Furthmore, we derive the up and low bound of a posteriori error estima-tors for these approximations, which means that the estimators are efficient and reliable. Numerical experiments confirm our conclusions.