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Two-Scale Picard Stabilized Finite Volume Method for the Incompressible Flow

Published online by Cambridge University Press:  03 June 2015

Jianhong Yang ,
Gang Lei  and
Jianwei Yang
Jianhong Yang*
Affiliation:
Department of Mathematics, Baoji University of Arts and Sciences, Baoji 721013, China
Gang Lei
Affiliation:
Department of Mathematics, Baoji University of Arts and Sciences, Baoji 721013, China
Jianwei Yang
Affiliation:
Department of Computer and Science, Baoji University of Arts and Sciences, Baoji 721007, China
*
*Corresponding author. Email: jianhongy [email protected]
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Abstract

In this paper, we consider a two-scale stabilized finite volume method for the two-dimensional stationary incompressible flow approximated by the lowest equal-order element pair P1 — P1 which do not satisfy the inf-sup condition. The two-scale method consist of solving a small non-linear system on the coarse mesh and then solving a linear Stokes equations on the fine mesh. Convergence of the optimal order in the H1-norm for velocity and the L2-norm for pressure are obtained. The error analysis shows there is the same convergence rate between the two-scale stabilized finite volume solution and the usual stabilized finite volume solution on a fine mesh with relation h = 𝾪 (H2). Numerical experiments completely confirm theoretic results. Therefore, this method presented in this paper is of practical importance in scientific computation.

Keywords

35Q1065N3076D05Incompressible flowstabilized finite volume methodinf-sup conditionlocal Gauss integraltwo-scale method
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 6 , Issue 5 , October 2014 , pp. 663 - 679
Copyright
Copyright © Global-Science Press 2014

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