Modified augmented Lagrangian preconditioners for the incompressible Navier–Stokes equations

We study different variants of the augmented Lagrangian (AL)‐based block‐triangular preconditioner introduced by the first two authors in SIAM J. Sci. Comput. 2006; 28 : 2095–2113]. The preconditioners are used to accelerate the convergence of the Generalized Minimal Residual method (GMRES) applied to various finite element and Marker‐and‐Cell discretizations of the Oseen problem in two and three space dimensions. Both steady and unsteady problems are considered. Numerical experiments show the effectiveness of the proposed preconditioners for a wide range of problem parameters. Implementation on parallel architectures is also considered. The AL‐based approach is further generalized to deal with linear systems from stabilized finite element discretizations. Copyright © 2010 John Wiley & Sons, Ltd.