Adaptive finite elements for optimally controlled elliptic variational inequalities of obstacle type
- In the recent past the adaptive finite element method has proved to be successfully applicable for the efficient numerical solution of a large number of problems. The main focus of this thesis lies in the development of an adaptive finite element scheme based on a standard residual-type a posteriori error estimate for the numerical solution of distributed optimal control problems for second order elliptic variational inequalities of obstacle type. As one of the main results, a convergence result is proven for a sequence of discrete C-stationary points. Furthermore, the residual-type a posteriori error estimator is shown to be reliable and efficient. Particular emphasis is put on the approximation of the reliability and efficiency related consistency errors. A detailed documentation of numerical results for a selection of test examples illustrates the performance of the adaptive approach.
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| Author: | Alexandra GaevskayaGND |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-24970 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/2497 |
| Advisor: | Ronald H. W. Hoppe |
| Type: | Doctoral Thesis |
| Language: | English |
| Publishing Institution: | Universität Augsburg |
| Granting Institution: | Universität Augsburg, Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Date of final exam: | 2013/07/24 |
| Release Date: | 2013/12/10 |
| Tag: | optimal control; elliptic variational inequalities; stationarity; finite elements; a posteriori error analysis |
| GND-Keyword: | Optimale Kontrolle; Elliptische Variationsungleichung; Finite-Elemente-Methode; Fehlerabschätzung; A-posteriori-Abschätzung |
| Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Licence (German): |  Deutsches Urheberrecht |
