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

In this paper,we consider a two-scale stabilized finite volume method for the two-dimensional stationary incompressible flow approximated by the lowest equalorder 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 H1-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=O(H^(2)).Numerical experiments completely confirm theoretic results.Therefore,this method presented in this paper is of practical importance in scientific computation.