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Adaptive finite element methods for computing nonstationary incompressible flows. (English) Zbl 1197.76002

Heidelberg: Univ. Heidelberg, Naturwissenschaftlich-Mathematische Gesamtfakultät (Diss.). ii, 178 p. (2009).
The rough contents of this impressive Ph. D. thesis are as follows: 1. Introduction; 2. Theoretical results; 3. Space-time finite element discretization; 4. A posteriori error estimation; 5. Issues on dynamic meshes; 6. Application and bibliography. The main aim is the development and analysis of efficient discretization methods able to provide accurate numerical solutions to three-dimensional nonstationary incompressible flow problems. The novelty of the work is the development of some a posteriori error estimators for the above flow problems which separate and quantitatively assess the temporal and spatial discretization errors. This allows the construction of efficient discretization methods because the temporal and spatial discretization errors can be balanced.

MSC:

76-02 Research exposition (monographs, survey articles) pertaining to fluid mechanics
76M10 Finite element methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
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