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2012 An Oseen Two-Level Stabilized Mixed Finite-Element Method for the 2D/3D Stationary Navier-Stokes Equations
Aiwen Wang, Xin Zhao, Peihua Qin, Dongxiu Xie
Abstr. Appl. Anal. 2012(SI12): 1-12 (2012). DOI: 10.1155/2012/520818

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., Q 1 P 0 and P 1 P 0 ). 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 ( u h , p h ) 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.

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Aiwen Wang. Xin Zhao. Peihua Qin. Dongxiu Xie. "An Oseen Two-Level Stabilized Mixed Finite-Element Method for the 2D/3D Stationary Navier-Stokes Equations." Abstr. Appl. Anal. 2012 (SI12) 1 - 12, 2012. https://doi.org/10.1155/2012/520818

Information

Published: 2012
First available in Project Euclid: 1 April 2013

zbMATH: 1237.76075
MathSciNet: MR2910713
Digital Object Identifier: 10.1155/2012/520818

Rights: Copyright © 2012 Hindawi

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Vol.2012 • No. SI12 • 2012
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