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.
Author: | Alexandra GaevskayaGND |
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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 |