Goal-oriented adaptivity in pointwise state constrained optimal control of partial differential equations
- Primal-dual-weighted goal-oriented a posteriori error estimates for pointwise state constrained optimal control problems for second order elliptic partial differential equations are derived. The constraints give rise to a primal-dual weighted error term representing the mismatch in the complementarity system due to discretization. In the case of sufficiently regular active (or coincidence) sets and problem data, a further decomposition of the multiplier into a regular L2-part on the active set and a singular part concentrated on the boundary between the active and inactive set allows to further characterize the mismatch error. The paper ends by a report on the behavior of the error estimates for test cases including the case of singular active sets consisting of smooth curves or points, only.
| Author: | Michael HintermüllerGND, Ronald H. W. HoppeORCiDGND |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-10801 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/1280 |
| Series (Serial Number): | Preprints des Instituts für Mathematik der Universität Augsburg (2009-16) |
| Type: | Preprint |
| Language: | English |
| Date of Publication (online): | 2009/06/25 |
| Publishing Institution: | Universität Augsburg |
| Contributing Corporation: | University of Houston, Humboldt Universität Berlin, Universität Graz |
| Release Date: | 2009/06/25 |
| Tag: | a posteriori error analysis; goal oriented dual weighted residuals; mesh adaptivity; optimal control; state constraints |
| GND-Keyword: | Elliptische Differentialgleichung; Optimale Kontrolle; 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 |
