On block preconditioners for nonsymmetric saddle point problems

We discuss a class of preconditioning methods for an iterative solution of algebraic nonsymmetric saddle point problems arising from a mixed finite element discretization of partial differential equations, in particular the Navier Stokes equation. We prove that block diagonal and block triangular preconditioners based on symmetric, positive definite blocks guarantee that the convergence rate of the method is independent of the mesh parameter h.