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L∞-Estimates for Approximated Optimal Control Problems

Meyer, Christian; Roesch, Arnd

Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin

An optimal control problem for a 2-d elliptic equation is investigated with pointwise control constraints. This paper is concerned with the discretization of the control by piecewise linear functions. The state and the adjoint state are discretized by linear finite elements. Approximation of order $h$ in the $L^\infty$-norm is proved in the main result. The theoretical result is confirmed by a numerical test.