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An adaptive numerical method for semi-infinite elliptic control problems based on error estimates

Abstract:

We discuss numerical reduction methods for an optimal control problem of semi-infinite type with finitely many control parameters but infinitely many constraints. We invoke known a priori error estimates to reduce the number of constraints. In a first strategy, we apply uniformly refined meshes, whereas in a second more heuristic strategy we use adaptive mesh refinement and provide an a posteriori error estimate for the control based on perturbation arguments.