A priori estimates for optimal Dirichlet boundary control problems |
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| Authors: | Klaus Deckelnick Andreas Günther Michael Hinze |
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| Institution: | 1. Institut für Analysis und Numerik, Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, 39106 Magdeburg, Germany;2. Bereich Optimierung und Approximation, Universität Hamburg, Bundesstraße 55, 20146 Hamburg, Germany |
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| Abstract: | We consider variational discretization of control constrained elliptic Dirichlet boundary control problems on smooth twoand three-dimensional domains, where we take into account the domain approximation. The state is discretized by linear finite elements, while the control variable is not discretized. We obtain optimal error bounds for the optimal control in two and three space dimensions. Furthermore we prove a superconvergence result in two space dimensions under the assumption that the underlying finite element meshes satisfy certain regularity requirements. We confirm our findings by a numerical experiment. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) |
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