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.

Download full text files

Export metadata

Statistics

Number of document requests

Additional Services

Share in Twitter Search Google Scholar
Metadaten
Author:Michael HintermüllerGND, Ronald H. W. HoppeORCiDGND, Caroline Löbhard
URN:urn:nbn:de:bvb:384-opus4-20600
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/2060
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Augsburg (2012-09)
Type:Preprint
Language:English
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