A priori error estimates for elliptic optimal control problems with a bilinear state equation

Authors:
Axel Kröner;Boris Vexler
Affiliations:
Technische Universität München, Zentrum Mathematik, Boltzmannstr. 3, 85748 Garching b. München, Germany;Technische Universität München, Zentrum Mathematik, Boltzmannstr. 3, 85748 Garching b. München, Germany
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

In this paper a priori error analysis for the finite element discretization of an optimal control problem governed by an elliptic state equation is considered. The control variable enters the state equation as a coefficient and is subject to pointwise inequality constraints. We derive a priori error estimates for the discretization error in the control variable and confirm our theoretical results by numerical examples.