A Dual-Weighted Residual Approach to Goal-Oriented Adaptivity for Optimal Control of Elliptic Variational Inequalities

  • A dual-weighted residual approach for goal-oriented adaptive finite elements for a class of optimal control problems for elliptic variational inequalities is studied. The development is based on the concept of C-stationarity. The overall error representation depends on primal residuals weighted by approximate dual quantities and vice versa as well as various complementarity mismatch errors. Also, a priori bounds for C-stationary points and associated multipliers are derived. Details on the numerical realization of the adaptive concept are provided and a report on numerical tests including the critical cases of biactivity are presented.

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Author:Michael HintermüllerGND, Ronald H. W. HoppeORCiDGND, Caroline Löbhard
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/2060
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Augsburg (2012-09)
Publishing Institution:Universität Augsburg
Contributing Corporation:Humboldt Universität Berlin
Release Date:2012/10/02
Tag:adaptive finite elements; goal-oriented error estimation; C-stationarity; mathematical programming with equilibrium constraints; optimal control of elliptic variational inequalities
GND-Keyword:Optimale Kontrolle; Elliptische Variationsungleichung; Fehlerabschätzung; Finite-Elemente-Methode
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