Preconditioning Linear Saddle Point Problems

In this paper we discuss how certain saddle point problems, arising from discretizations of partial differential equations, should be preconditioned in order to obtain iterative methods which converge with a rate independent of the discretization parameters. The results for the discrete systems are motivated from corresponding results for the continuous systems. Our general approach is illustrated by studying Stokes’ problem, a mixed formulation of second order elliptic equations and a variational problem motivated from scattered data approximation.