TY - JOUR T1 - Two-Scale Picard Stabilized Finite Volume Method for the Incompressible Flow AU - Yang , Jianhong AU - Gang , Lei AU - Yang , Jianwei JO - Advances in Applied Mathematics and Mechanics VL - 5 SP - 663 EP - 679 PY - 2014 DA - 2014/06 SN - 6 DO - http://doi.org/10.4208/aamm.2013.m153 UR - https://global-sci.org/intro/article_detail/aamm/41.html KW - Incompressible flow, stabilized finite volume method, inf-sup condition, local Gauss integral, two-scale method. AB -

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.