Exponential Convergence of hp-Finite Element Discretization of Optimal Boundary Control Problems with Elliptic Partial Differential Equations

We investigate the numerical solution of a boundary control problem with elliptic partial differential equation by the hp-finite element method. We prove exponential convergence with respect to the number of unknowns for an a-priori chosen discretization. Here, we have to prove that derivatives of arbitrary order of the solution are in suitably chosen weighted Sobolev spaces. Numerical experiments confirm the theoretical findings.