@Article{AAMM-6-5,
author = {Yang, Jianhong and Lei, Gang and Yang, Jianwei},
title = {Two-Scale Picard Stabilized Finite Volume Method for the Incompressible Flow},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2014},
volume = {6},
number = {5},
pages = {663--679},
abstract = {<p style="text-align: justify;">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 &nbsp;$h =\mathcal{O}(H^2)$. &nbsp;Numerical experiments completely
confirm theoretic results. Therefore, this method presented in this paper is of practical importance in
scientific computation.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.2013.m153},
url = {https://global-sci.com/article/73463/two-scale-picard-stabilized-finite-volume-method-for-the-incompressible-flow}
}