TABLE OF CONTENTS The finite element method (FEM) is a modern and efficient technique for the numerical solution of partial differential equations. It is based on the so-called variational formulation of the problem under consideration, represented by an integral identity satisfied for suitable test functions, and on the piecewise polynomial approximation of the sought solution. A detailed theoretical treatment and numerous applications of the FEM are the subject of thousands of papers and a number of books. From this extensive literature let us mention a few monographs, such as (Babu ka and Strouboulis, 2001), (Brenner and Scott, 1994), (Ciarlet, 1979), (Girault and Raviart, 1979), (Girault and Raviart, 1986), (Glowinski, 1984), (Hinton and Owen, 1977), (Johnson, 1987), (K? ek and Neittaanm ki, 1990), (Pironneau, 1989), (Quarteroni and Valli, 1997), (Schwab, 1998), (Strang and Fix, 1973), (Szabo and Babu ka, 1991), (Thom e, 1997), ( en ek, 1990), (Zienkiewicz and Morgan, 1983).
There is a widely held opinion that finite element techniques should be mainly used for the solution of problems with large diffusion and solid mechanics problems, whereas the finite volume method is more suitable for problems with small or vanishing diffusion and fluid dynamics problems. However, the FEM scores a considerable success also in CFD.
Concerning the FE solution of incompressible viscous flow (incompressible Navier-Stokes equations), there are the well-known monographs (Temam, 1977), (Girault and Raviart, 1979), (Girault and Raviart, 1986), (Gresho and Sani, 2000), (Turek, 1999). Most specialists prefer to use the so-called conforming finite elements which yield approximate solutions continuous in...
