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 |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-20600 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/2060 |
| Series (Serial Number): | Preprints des Instituts für Mathematik der Universität Augsburg (2012-09) |
| Type: | Preprint |
| Language: | English |
| Date of Publication (online): | 2012/10/02 |
| Publishing Institution: | Universität Augsburg |
| Contributing Corporation: | Humboldt Universität Berlin |
| Release Date: | 2012/10/02 |
| Tag: | C-stationarity; adaptive finite elements; goal-oriented error estimation; 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 |
