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The Scientific World Journal
Volume 2013 (2013), Article ID 486323, 6 pages
http://dx.doi.org/10.1155/2013/486323
Research Article

Incomplete Augmented Lagrangian Preconditioner for Steady Incompressible Navier-Stokes Equations

1School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, China
2Department of Information and Computational Science, Chengdu Technological University, Chengdu, Sichuan 611730, China

Received 16 July 2013; Accepted 29 August 2013

Academic Editors: I. Altun, S. Amat, and S. Hristova

Copyright © 2013 Ning-Bo Tan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

An incomplete augmented Lagrangian preconditioner, for the steady incompressible Navier-Stokes equations discretized by stable finite elements, is proposed. The eigenvalues of the preconditioned matrix are analyzed. Numerical experiments show that the incomplete augmented Lagrangian-based preconditioner proposed is very robust and performs quite well by the Picard linearization or the Newton linearization over a wide range of values of the viscosity on both uniform and stretched grids.