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

Published online by Cambridge University Press:  03 June 2015

Tong Zhang  and
Shunwei Xu
Tong Zhang*
Affiliation:
School of Mathematics & Information Science, Henan Polytechnic University, Jiaozuo 454003, Henan, China
Shunwei Xu*
Affiliation:
School of Mathematics & Information Science, Henan Polytechnic University, Jiaozuo 454003, Henan, China
*
Corresponding author.Email: [email protected]
Email: [email protected]
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Abstract

In this work, two-level stabilized finite volume formulations for the 2D steady Navier-Stokes equations are considered. These methods are based on the local Gauss integration technique and the lowest equal-order finite element pair. Moreover, the two-level stabilized finite volume methods involve solving one small Navier-Stokes problem on a coarse mesh with mesh size H, a large general Stokes problem for the Simple and Oseen two-level stabilized finite volume methods on the fine mesh with mesh size or a large general Stokes equations for the Newton two-level stabilized finite volume method on a fine mesh with mesh size . These methods we studied provide an approximate solution with the convergence rate of same order as the standard stabilized finite volume method, which involve solving one large nonlinear problem on a fine mesh with mesh size h. Hence, our methods can save a large amount of computational time.

Keywords

65N3065N0876D05Stationary Navier-Stokes equationsfinite volume methodtwo-level methoderror estimate
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 5 , Issue 1 , February 2013 , pp. 19 - 35
Copyright
Copyright © Global-Science Press 2013

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