Goal-oriented adaptivity in control constrained optimal control of partial differential equations

  • Dual-weighted goal-oriented error estimates for a class of pointwise control constrained optimal control problems for second order elliptic partial differential equations are derived. It is demonstrated that the constraints give rise to a primal-dual weighted error term representing the mismatch in the complementarity system due to discretization. Also, for the new error estimate a posteriori error estimators for the L²-norm of the solution and its adjoint are derived.

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Author:Michael HintermüllerGND, Ronald H. W. HoppeORCiDGND
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/520
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Augsburg (2007-13)
Publishing Institution:Universität Augsburg
Contributing Corporation:Department of Mathematics, University of Houston
Release Date:2007/05/30
Tag:goal oriented dual weighted approach; optimal control; control constraints; a posteriori error estimate; PDE-constrained optimization
GND-Keyword:Optimale Kontrolle; A-posteriori-Abschätzung; Fehleranalyse; Elliptische Differentialgleichung
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Numerische Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik