A two-level finite volume method for the unsteady Navier-Stokes equations based on two local Gauss integrations

Authors:
Tong Zhang;Jinhua Yang
Affiliations:
-;-
Venue:
Journal of Computational and Applied Mathematics
Year:
2014

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Abstract

In this paper we consider a two-level finite volume method for the two-dimensional unsteady Navier-Stokes equations by using two local Gauss integrations. This new stabilized finite volume method is based on the linear mixed finite element spaces. Some new a priori bounds for the approximate solution are derived. Moreover, a two-level stabilized finite volume method involves solving one small Navier-Stokes problem on a coarse mesh with mesh size H, a large general Stokes problem on the fine mesh with mesh size h@?H. The optimal error estimates of the H^1-norm for velocity approximation and the L^2-norm for pressure approximation are established. If we choose h=O(H^2), the two-level method gives the same order of approximation as the one-level stabilized finite volume method. However, our method can save a large amount of computational time.