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Goal-Oriented Adaptivity in Space-Time Finite Element Simulations of Nonstationary Incompressible Flows

Besier, Michael

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Abstract

Subject of this paper is the development of an a posteriori error estimator for nonstationary incompressible flow problems. The error estimator is computable and able to assess the temporal and spatial discretization errors separately. Thereby, the error is measured in an arbitrary quantity of interest because measuring errors in global norms is often of minor importance in practical applications. The basis for this is a finite element discretization in time and space. The techniques presented here also provide local error indicators which are used to adaptively refine the temporal and spatial discretization. A key ingredient in setting up an efficient discretization method is balancing the error contributions due to temporal and spatial discretization. To this end, a quantitative assessment of the individual discretization errors is required. The described method is validated by an established Navier-Stokes benchmark.

Item Type: Preprint
Series Name: IWR-Preprints
Date Deposited: 18. Oct 2010 11:35
Date: 2010
Faculties / Institutes: Service facilities > Interdisciplinary Center for Scientific Computing
Subjects: 510 Mathematics
Controlled Keywords: Numerische Strömungssimulation, Navier-Stokes-Gleichung, Finite-Elemente-Methode, Galerkin-Methode, A-posteriori-Abschätzung, Adaptives Verfahren
Uncontrolled Keywords: Orts-Zeit-Finite-Elemente-Methode , zielorientierte a posteriori-Fehlerschätzungnonstationary incompressible flows , space-time finite element methods , goal-oriented a posteriori error estimation , adaptivity
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