Adaptive finite element methods for computing nonstationary incompressible flows [Elektronische Ressource] / vorgelegt von Michael Schmich

Inaugural-DissertationzurErlangung der DoktorwürdederNaturwissenschaftlich-Mathematischen GesamtfakultätderRuprecht-Karls-UniversitätHeidelbergvorgelegt vonDiplom-Mathematiker Michael Schmichaus MannheimTag der mündlichen Prüfung: 15. Dezember 2009Adaptive Finite Element Methods forComputing Nonstationary IncompressibleFlowsGutachter: Prof. Dr. Dr. h.c. Rolf RannacherProf. Dr. Peter BastianAbstractSubject of this work is the development of numerical methods for efficiently solving nonstationaryincompressible flow problems. In contrast to stationary flow problems, here errors due to discretiza-tion in time and space occur. Furthermore, especially three-dimensional simulations lead to hugecomputational costs. Thus, adaptive discretization methods have to be used in order to reduce the costs while still maintaining a certain accuracy.The main focus of this thesis is the development of an a posteriori error estimator which iscomputable and able to assess both discretization errors separately. Thereby, the error is measuredin an arbitrary quantity of interest (such as the drag-coefficient, for example) because measuringerrors in global norms is often of minor importance in practical applications. The basis for this is afinite element discretization in time and space. The techniques presented here also provide localerror indicators which are used to adaptively refine the temporal and spatial discretization.