Fast nonsymmetric iterations and preconditioning for Navier-Stokes equations
SIAM Journal on Scientific Computing - Special issue on iterative methods in numerical linear algebra; selected papers from the Colorado conference
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Analysis of Preconditioners for Saddle-Point Problems
SIAM Journal on Scientific Computing
An Augmented Lagrangian-Based Approach to the Oseen Problem
SIAM Journal on Scientific Computing
An Augmented Lagrangian Approach to Linearized Problems in Hydrodynamic Stability
SIAM Journal on Scientific Computing
Stabilized finite element schemes with LBB-stable elements for incompressible flows
Journal of Computational and Applied Mathematics
SIAM Journal on Scientific Computing
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We study a block triangular preconditioner for finite element approximations of the linearized Navier-Stokes equations. The preconditioner is based on the augmented Lagrangian formulation of the problem and was introduced by the authors in [SIAM J. Sci. Comput., 28 (2006), pp. 2095-2113]. In this paper we prove field-of-values type estimates for the preconditioned system which lead to optimal convergence bounds for the GMRES algorithm applied to solve the system. Two variants of the preconditioner are considered: an ideal one based on exact solves for the velocity submatrix, and a more practical variant based on block triangular approximations of the velocity submatrix.