Two-Level Stabilized Finite Volume Methods for Stationary Navier-Stokes Equations. (7th May 2012)

• Record Type: Journal Article
• Authors: Rachid, Anas; Bahaj, Mohamed; Ayoub, Noureddine
• Other Names: Han Weimin Academic Editor.
• Is Part Of: Advances in numerical analysis. Volume 2012(2012)
• Publication Date: 2012-05-07
• Subjects: Numerical analysis -- Periodicals; Numerical analysis; Periodicals; Electronic journals; 518
• DOI: 10.1155/2012/309871
• Languages: English
• ISSNs: 1687-9562

Abstract

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.