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 an integral constraint for the state with Neumann-edge,with the constraints K = {y∈H¹(Ω):∫_(?)Ωy≥γ}.we derive the optimality conditions of the control problem.The finite element approximations are constructed on multi-meshes,which are suitable to treat different regularities of the control and state,and the optimality conditions of the discrete system is given.Furthmore,we derive and prove the priori error estimates , at the same time, an optimal posteriori error estimator for the element approximation is obtained.