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.
Download full text files
Statistics
Print On Demand
Additional Services
| Author: | Michael HintermüllerGND, Michael Hinze, Ronald H. W. HoppeORCiDGND |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-11761 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/1440 |
| Series (Serial Number): | Preprints des Instituts für Mathematik der Universität Augsburg (2010-12) |
| Type: | Preprint |
| Language: | English |
| Date of Publication (online): | 2010/09/22 |
| 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; adaptive finite elements; elliptic optimal control; gradient state-constraints |
| 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 |
