Year: 2014
Author: Jianhong Yang, Lei Gang, Jianwei Yang
Advances in Applied Mathematics and Mechanics, Vol. 6 (2014), Iss. 5 : pp. 663–679
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 $P_1-P_1$ which does not satisfy the inf-sup condition. The two-scale method consists 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 $H^1$-norm for velocity and the $L^2$-norm for pressure is 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 $h =\mathcal{O}(H^2)$. Numerical experiments completely confirm theoretic results. Therefore, this method presented in this paper is of practical importance in scientific computation.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.2013.m153
Advances in Applied Mathematics and Mechanics, Vol. 6 (2014), Iss. 5 : pp. 663–679
Published online: 2014-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Incompressible flow stabilized finite volume method inf-sup condition local Gauss integral two-scale method.