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
Frontdoor URL
Advisor:Ronald H. W. Hoppe
Type:Doctoral Thesis
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