A block preconditioner for high-order mixed finite element approximations to the Navier-Stokes equations

An iterative solver for the linear system arising from a discretization by high-order mixed finite elements for the linearized steady state Navier - Stokes problem is presented. Two mixed finite elements are considered: Pk+1Pk and Pk+2Pk. The iterative solver is based on the GMRES method with right preconditioning where the preconditioner has a block upper triangular form. Computational results show that the convergence rate seems to be independent of the grid size parameter h and the polynomial degree k but is slightly affected by the increasing of the Reynolds number.