Title :

A preconditioner for generalized saddle point problems: application to 3D stationary Navier-Stokes equations

Author(s) :

Calgaro, Caterina [Auteur]
SImulations and Modeling for PArticles and Fluids [SIMPAF]
Deuring, Paul [Auteur]
Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville [LMPA]
Jennequin, Delphine [Auteur]
SImulations and Modeling for PArticles and Fluids [SIMPAF]

Journal title :

Numerical Methods for Partial Differential Equations

Pages :

1289--1313

Publisher :

Wiley

Publication date :

2006

ISSN :

0749-159X

HAL domain(s) :

Mathématiques [math]/Analyse numérique [math.NA]

English abstract : [en]

In this article we consider the stationary Navier‐Stokes system discretized by finite element methods which do not satisfy the inf‐sup condition. These discretizations typically take the form of a variational problem with ...
Show more >In this article we consider the stationary Navier‐Stokes system discretized by finite element methods which do not satisfy the inf‐sup condition. These discretizations typically take the form of a variational problem with stabilization terms. Such a problem may be transformed by iteration methods into a sequence of linear, Oseen‐type variational problems. On the algebraic level, these problems belong to a certain class of linear systems with nonsymmetric system matrices (“generalized saddle point problems”). We show that if the underlying finite element spaces satisfy a generalized inf‐sup condition, these problems have a unique solution. Moreover, we introduce a block triangular preconditioner and we show how the eigenvalue bounds of the preconditioned system matrix depend on the coercivity constant and continuity bounds of the bilinear forms arising in the variational problem. Finally we prove that the stabilized P1‐P1 finite element method proposed by Rebollo is covered by our theory and we show that the condition number of the preconditioned system matrix is independent of the mesh size. Numerical tests with 3D stationary Navier‐Stokes flows confirm our results.Show less >

Language :

Anglais

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL