An a posteriori error analysis of adaptive finite element methods for distributed elliptic control problems with control constraints
- We present an a posteriori error analysis of adaptive finite element approximations of distributed control problems for second order elliptic boundary value problems under bound constraints on the control. The error analysis is based on a residual-type a posteriori error estimator that consists of edge and element residuals. Since we do not assume any regularity of the data of the problem, the error analysis further invokes data oscillations. We prove reliability and efficiency of the error estimator and provide a bulk criterion for mesh refinement that also takes into account data oscillations and is realized by a greedy algorithm. A detailed documentation of numerical results for selected test problems illustrates the convergence of the adaptive finite element method.
| Author: | Michael HintermüllerGND, Ronald H. W. HoppeORCiDGND, Yuri IliashGND, Michael KiewegGND |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-4235 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/522 |
| Series (Serial Number): | Preprints des Instituts für Mathematik der Universität Augsburg (2007-14) |
| Type: | Preprint |
| Language: | English |
| Date of Publication (online): | 2007/05/30 |
| Publishing Institution: | Universität Augsburg |
| Contributing Corporation: | Department of Mathematics, University of Houston |
| Release Date: | 2007/05/30 |
| Tag: | a posteriori error analysis; adaptive finite elements; control constraints; distributed control |
| 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 |
