An energy space finite element approach for elliptic Dirichlet boundary control problems

In this paper we present a finite element analysis for a Dirichlet boundary control problem where the Dirichlet control is considered in the energy space H1/2(Γ). As an equivalent norm in H1/2(Γ) we use a norm which is induced by a stabilized hypersingular boundary integral operator. The analysis is based on the mapping properties of the solution operators related to the primal and adjoint boundary value problems, and their finite element approximations. Some numerical results are given.