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A TWO-LEVEL DEFECT–CORRECTION METHOD FOR NAVIER–STOKES EQUATIONS

Part of: Equations of mathematical physics and other areas of application Partial differential equations, boundary value problems

Published online by Cambridge University Press:  21 October 2009

QINGFANG LIU  and
YANREN HOU
QINGFANG LIU*
Affiliation:
School of Science, Xi’an Jiaotong University, Xi’an 710049, PR China (email: qfliu08@hotmail.com)
YANREN HOU
Affiliation:
School of Science, Xi’an Jiaotong University, Xi’an 710049, PR China (email: yrhou@mail.xjtu.edu.cn)
*
✉For correspondence; e-mail: qfliu08@hotmail.com
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Abstract

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A two-level defect–correction method for the steady-state Navier–Stokes equations with a high Reynolds number is considered in this paper. The defect step is accomplished in a coarse-level subspace Hm by solving the standard Galerkin equation with an artificial viscosity parameter σ as a stability factor, and the correction step is performed in a fine-level subspace HM by solving a linear equation. H1 error estimates are derived for this two-level defect–correction method. Moreover, some numerical examples are presented to show that the two-level defect–correction method can reach the same accuracy as the standard Galerkin method in fine-level subspace HM. However, the two-level method will involve much less work than the one-level method.

Keywords

two-level methoddefect–correction methodspectral methodNavier–Stokes equations

MSC classification

Secondary: 65N35: Spectral, collocation and related methods 35Q30: Navier-Stokes equations
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 81 , Issue 3 , June 2010 , pp. 442 - 454
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2009

Footnotes

Subsidized by NSF of China (Grant No. 10471110, No. 10871156) and NCET.

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