A posteriori error estimation of finite element approximations of pointwise state constrained distributed control problems
- We provide an a posteriori error analysis of finite element approximations of pointwise state constrained distributed optimal control problems for second order elliptic boundary value problems. In particular, we derive a residual-type a posteriori error estimator and prove its efficiency and reliability up to oscillations in the data of the problem and a consistency error term. In contrast to the case of pointwise control constraints, the analysis is more complicated, since the multipliers associated with the state constraints live in measure spaces. The analysis essentially makes use of appropriate regularizations of the multipliers both in the continuous and in the discrete regime. Numerical examples are given to illustrate the performance of the error estimator.
| Author: | Ronald H. W. HoppeORCiDGND, Michael KiewegGND |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-4351 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/541 |
| Series (Serial Number): | Preprints des Instituts für Mathematik der Universität Augsburg (2007-16) |
| Type: | Preprint |
| Language: | English |
| Publishing Institution: | Universität Augsburg |
| Contributing Corporation: | Department of Mathematics, University of Houston |
| Release Date: | 2007/07/02 |
| Tag: | optimal control; pointwise state constraints; adaptive finite element methods |
| GND-Keyword: | Optimale Kontrolle; Finite-Elemente-Methode; A-posteriori-Abschätzung; Fehleranalyse; Elliptisches Randwertproblem |
| 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 |
