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Published in:
2011 | OriginalPaper | Chapter
Finite element discretization
Authors : Sven Gross, Arnold Reusken
Published in: Numerical Methods for Two-phase Incompressible Flows
Publisher: Springer Berlin Heidelberg
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In this chapter we treat finite element methods for the discretization of the variational Oseen problem (2.21) and for the
spatial
discretization of the variational formulation of the non-stationary Stokes- and Navier-Stokes equations. We restrict ourselves to the class of Hood-Taylor finite elements on tetrahedral grids. In order to perform local grid refinement/coarsening in an efficient way, which is very important in two-phase flow applications, and to be able to use fast multigrid iterative solution methods we will apply such finite element methods not on one grid but on a
hierarchy of nested triangulations
. The construction of such a multilevel grid hierarchy is discussed in Sect. 3.1. In Sect. 3.2 the Hood-Taylor finite element spaces are treated. We present a numerical example in Sect. 3.3, where the approximation order of such a Hood-Taylor finite element space is investigated.