Goal-oriented adaptivity in control constrained optimal control of partial differential equations
- Dual-weighted goal-oriented error estimates for a class of pointwise control constrained optimal control problems for second order elliptic partial differential equations are derived. It is demonstrated that the constraints give rise to a primal-dual weighted error term representing the mismatch in the complementarity system due to discretization. Also, for the new error estimate a posteriori error estimators for the L²-norm of the solution and its adjoint are derived.
| Author: | Michael HintermüllerGND, Ronald H. W. HoppeORCiDGND |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-4212 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/520 |
| Series (Serial Number): | Preprints des Instituts für Mathematik der Universität Augsburg (2007-13) |
| Type: | Preprint |
| Language: | English |
| Publishing Institution: | Universität Augsburg |
| Contributing Corporation: | Department of Mathematics, University of Houston |
| Release Date: | 2007/05/30 |
| Tag: | goal oriented dual weighted approach; optimal control; control constraints; a posteriori error estimate; PDE-constrained optimization |
| GND-Keyword: | Optimale Kontrolle; A-posteriori-Abschätzung; Fehleranalyse; Elliptische Differentialgleichung |
| 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 |
