This thesis deals with the optimal control of PDEs. After a brief introduction in the theory of elliptic and parabolic PDEs, we introduce a software that solves systems of PDEs by the finite elements method. In the second chapter we derive optimality conditions in terms of function spaces, i.e. a systems of PDEs coupled by some pointwise relations. Now we present algorithms to solve the optimality systems numerically and present some numerical test cases. A further chapter deals with the so called lack of adjointness, an issue of gradient methods applied on parabolic optimal control problems. However, since optimal control problems lead to large numerical schemes, model reduction becomes popular. We analyze the proper orthogonal decomposition method and apply it to our model problems. Finally, we apply all considered techniques to a real world problem.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa.de:bsz:105-qucosa-204639 |
| Date | 23 June 2016 |
| Creators | Prüfert, Uwe |
| Contributors | Technische Universität Bergakademie Freiberg, Mathematik und Informatik, Prof. Dr. rer. nat habil. Michael Eiermann, Prof. Dr. rer. nat. habil. Michael Eiermann, Prof. Dr. rer. nat. habil. Thomas Slawig, Prof. Dr. rer. nat. Christian Meyer |
| Publisher | Technische Universitaet Bergakademie Freiberg Universitaetsbibliothek "Georgius Agricola" |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | doc-type:doctoralThesis |
| Format | application/pdf |
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