The scope ofthis book is to discuss recent numerical and algorithmic tools for the solution of certain flow problems arising in Computational Fluid Dynam­ ics (CFD). Here, we mainly restrict ourselves to the case of the incompressible Navier-Stokes equations, Ut - v~u + U . V'u+ V'p = f , V'·u = o. (1) These basic equations already play an important role in CFD, both for math­ ematicians as well as for more practical scientists: Physically important facts with "real life" character can be described by them, including also economical aspects in industrial applications. On the other hand, the equations in (1) provide the complete spectrum of numerical problems nowadays concerning the mathematical treatment of partial differential equations. Although this field of research may appear to be a small part only inside of CFD, it was and still is of great interest for mathematicians as well as engineers, physicists, computer scientists and many more: a fact which can be easily checked by counting the numerous publications. Nevertheless, our contribution has some unique characteristics since it contains a few of the lat­ est results for the numerical solution of (complex) flow problems on modern computer platforms. In this book, our particular emphasis lies on the solu­ tion process of the resulting high dimensional discrete systems ofequations which is often neglected in other works. Together with the included CDROM, which contains the 'FEATFLOW 1.