Discretization Error Estimates for an Optimal Control Problem in a Nonconvex Domain

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An optimal control problem for a 2-d elliptic equation and with pointwise control constraints is investigated. The domain is assumed to be polygonal but non-convex. The corner singularities are treated by a priori mesh grading. A second order approximation of the optimal control is constructed by a projection of the discrete adjoint state. Here we summarize the results from [1] and add further numerical tests.