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Preprint 22-2004

L^infty-Estimates for Approximated Optimal Control Problems

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Author(s) : Christian Meyer , Arnd Roesch

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 22-2004

MSC 2000

49K20 Problems involving partial differential equations
49M25 Discrete approximations

Abstract :
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.

Keywords : Linear-quadratic optimal control problems, error estimates, elliptic equations, numerical approximation, control constraints

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