Eigenvalue estimates for a preconditioned Galerkin matrix arising from mixed finite element discretizations of viscous incompressible flows

The article deals with Galerkin matrices arising with finite element discretizations of the Navier-Stokes system. Usually these matrices are indefinite and nonsymmetric. They have to be preconditioned if a related linear system is to be solved efficiently by an iterative method. We consider preconditioning by a pressure mass matrix. It is shown how upper and lower bounds of the eigenvalues of a preconditioned Galerkin matrix may be found by variational arguments.