Approximation of Boundary Control Problems on Curved Domains. Ii - the Dirichlet Case

Abstract. The influence of small boundary variations of the domain on optimal controls is investigated in this paper. The domain variations are governed by a small parameter h → 0. In a previous paper we have studied the Neuman control problem. In this paper, the Dirichlet control problem is considered. The optimal solutions are compared between the problems defined in the curved domain Ω and the polygonal domains Ωh, in the norm defined on the fixed boundary Γ = ∂Ω of the curved domain. To this end, an appropriate parametrization of the boundaries is introduced, and a one-to-one mapping between the boundaries Γ and Γh is employed. Error estimates of the order h in the norm on the fixed boundary Γ are derived for the difference of optimal controls.