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

  • Jianhong Yang (a1), Gang Lei (a1) and Jianwei Yang (a2)

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 P1P1 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 L2-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(H2). Numerical experiments completely confirm theoretic results. Therefore, this method presented in this paper is of practical importance in scientific computation.

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*Corresponding author. Email: jianhongy
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Advances in Applied Mathematics and Mechanics
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  • EISSN: 2075-1354
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