The Stokes Problem

Abstract

The purpose of this chapter is to introduce one of the “most prominent” sources of symmetric but indefinite linear systems. It stems from finite element (or finite volumes, finite differences, ...) discretizations of the Stokes equations. In a more general framework, the standard variational formulation of the Stokes equations turns out to be nothing but a saddle point problem. We will see that appropriate discretizations of such a problem lead to indefinite linear systems. It is precisely this problem class which motivated the search for stable and efficient solvers for symmetric but indefinite systems.