Finite element discretization

Abstract

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.