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Advances in Numerical Analysis
Volume 2012 (2012), Article ID 309871, 14 pages
http://dx.doi.org/10.1155/2012/309871
Research Article

Two-Level Stabilized Finite Volume Methods for Stationary Navier-Stokes Equations

1École Nationale Supérieure des Arts et Métiers-Casablanca, Université Hassan II, B.P. 150, Mohammedia, Morocco
2Department of Mathematics and Computing Sciences, Faculty of Sciences and Technology, University Hassan 1st, B.P. 577, Settat, Morocco

Received 17 December 2011; Accepted 17 February 2012

Academic Editor: Weimin Han

Copyright © 2012 Anas Rachid 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

We propose two algorithms of two-level methods for resolving the nonlinearity in the stabilized finite volume approximation of the Navier-Stokes equations describing the equilibrium flow of a viscous, incompressible fluid. A macroelement condition is introduced for constructing the local stabilized finite volume element formulation. Moreover the two-level methods consist of solving a small nonlinear system on the coarse mesh and then solving a linear system on the fine mesh. The error analysis shows that the two-level stabilized finite volume element method provides an approximate solution with the convergence rate of the same order as the usual stabilized finite volume element solution solving the Navier-Stokes equations on a fine mesh for a related choice of mesh widths.