Boundary concentrated finite elements for optimal control problems with distributed observation

We consider the discretization of an optimal boundary control problem with distributed observation by the boundary concentrated finite element method. If the constraint is a H 1 + δ ( Ω ) regular elliptic PDE with smooth differential operator and source term, we prove for the two dimensional case that the discretization error in the L 2 norm decreases like N - δ , where N is the number of unknowns. Our approach is suitable for solving a wide class of problems, among them piecewise defined data and tracking functionals acting only on a subdomain of Ω . We present several numerical results.