Abstract and Applied Analysis

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

Aiwen Wang, Xin Zhao, Peihua Qin, and Dongxiu Xie

Full-text: Open access

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.

Article information

Source
Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 520818, 12 pages.

Dates
First available in Project Euclid: 1 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1364845164

Digital Object Identifier
doi:10.1155/2012/520818

Mathematical Reviews number (MathSciNet)
MR2910713

Zentralblatt MATH identifier
1237.76075

Citation

Wang, Aiwen; Zhao, Xin; Qin, Peihua; Xie, Dongxiu. An Oseen Two-Level Stabilized Mixed Finite-Element Method for the 2D/3D Stationary Navier-Stokes Equations. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 520818, 12 pages. doi:10.1155/2012/520818. https://projecteuclid.org/euclid.aaa/1364845164


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