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Preprint 18-2003

Error estimates for parabolic optimal control problems with control constraints

Source file is available as :   Postscript Document

Author(s) : Arnd Rösch

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 18-2003

MSC 2000

49N10 Linear-quadratic problems
65K10 Optimization and variational techniques

Abstract :
An optimal control problem for the 1-d heat equation is investigated with pointwise control constraints. This paper is concerned with the discretization of the control by piecewise linear functions. The connection between the solutions of the discretized problems and the continuous one is investigated. Under an additional assumption on the adjoint state an approximation order $\sigma^{3/2}$ is proved for uniform discretizations. In the general case it is shown that a non-uniform control discretization ensure an approximation of order $\sigma^{3/2}$. Numerical tests confirm the theoretical part.

Keywords : Linear-quadratic optimal control problems, error estimates, heat equation, non-uniform grids, numerical approximation, control constraints.

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