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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 520818, 12 pages
http://dx.doi.org/10.1155/2012/520818
Research Article

An Oseen Two-Level Stabilized Mixed Finite-Element Method for the 2D/3D Stationary Navier-Stokes Equations

1Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China
2School of Applied Science, Beijing Information Science and Technology University, Beijing 100192, China
3Graduate University of Chinese Academy of Sciences, Beijing 100049, China
4Departement of Geographical Science and Environmental Engineering, Baoji University of Arts and Sciences, Baoji 721007, China

Received 1 December 2011; Accepted 28 January 2012

Academic Editor: Shaher Momani

Copyright © 2012 Aiwen Wang 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 investigate an Oseen two-level stabilized finite-element method based on the local pressure projection for the 2D/3D steady Navier-Stokes equations by the lowest order conforming finite-element pairs (i.e., Q1P0 and P1P0). Firstly, in contrast to other stabilized methods, they are parameter free, no calculation of higher-order derivatives and edge-based data structures, implemented at the element level with minimal cost. In addition, the Oseen two-level stabilized method involves solving one small nonlinear Navier-Stokes problem on the coarse mesh with mesh size H, a large general Stokes equation on the fine mesh with mesh size h=O(H)2. The Oseen two-level stabilized finite-element method provides an approximate solution (uh,ph) with the convergence rate of the same order as the usual stabilized finite-element solutions, which involves solving a large Navier-Stokes problem on a fine mesh with mesh size h. Therefore, the method presented in this paper can save a large amount of computational time. Finally, numerical tests confirm the theoretical results. Conclusion can be drawn that the Oseen two-level stabilized finite-element method is simple and efficient for solving the 2D/3D steady Navier-Stokes equations.