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A priori estimates for optimal Dirichlet boundary control problems
Author(s) -
Deckelnick Klaus,
Günther Andreas,
Hinze Michael
Publication year - 2009
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200910277
Subject(s) - discretization , mathematics , boundary (topology) , superconvergence , dirichlet boundary condition , a priori and a posteriori , finite element method , optimal control , dirichlet distribution , domain (mathematical analysis) , space (punctuation) , polygon mesh , mathematical analysis , boundary value problem , mathematical optimization , computer science , geometry , physics , philosophy , epistemology , thermodynamics , operating system
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)