Weak-duality based adaptive finite element methods for PDE-constrained optimization with pointwise gradient state-constraints

  • Adaptive finite element methods for optimization problems for second order linear elliptic partial differential equations subject to pointwise constraints on the l2-norm of the gradient of the state are considered. In a weak duality setting, i.e., without assuming a constraint qualification such as the existence of a Slater point, residual based a posteriori error estimators are derived. To overcome the lack in constraint qualification on the continuous level, the weak Fenchel dual is utilized. Several numerical tests illustrate the performance of the proposed error estimators.

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Author:Michael HintermüllerGND, Michael Hinze, Ronald H. W. HoppeGND
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/1440
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Augsburg (2010-12)
Publishing Institution:Universität Augsburg
Contributing Corporation:Humboldt-University of Berlin, University of Hamburg, University of Houston
Release Date:2010/09/22
Tag:PDE constrained optimization; elliptic optimal control; gradient state-constraints; adaptive finite elements
GND-Keyword:Optimale Kontrolle; Elliptische Differentialgleichung; Finite-Elemente-Methode; Fehleranalyse; A-posteriori-Abschätzung
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
Licence (German):Deutsches Urheberrecht mit Print on Demand