The considered steady-state Navier-Stokes problem is linearized by applying a fixed point iteration. The resulting linear Oseen problem within each iteration step is discretized by means of the mixed finite element method. This discretization leads to a nonsymmetric indefinite linear system of equations. Two preconditioners for such problems are proposed, and it is shown that the spectra of the preconditioned systems are bounded independently of the discretization parameter.
The linear systems of equations are solved by means of Krylov subspace iterative methods. Numerical experiments show that the convergence rate of these methods is independent of the discretization parameter. Furthermore, the application of inner iterations within the preconditioner is discussed.