Volume 6, Issue 5
Two-Scale Picard Stabilized Finite Volume Method for the Incompressible Flow

Adv. Appl. Math. Mech., 6 (2014), pp. 663-679.

Published online: 2014-06

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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 $P_1-P_1$ 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 $H^1$-norm for velocity and the $L^2$-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  $h =\mathcal{O}(H^2)$.  Numerical experiments completely confirm theoretic results. Therefore, this method presented in this paper is of practical importance in scientific computation.

• Keywords

Incompressible flow stabilized finite volume method {inf-sup} condition local Gauss integral two-scale method