A TWO-LEVEL FINITE ELEMENT GALERKIN METHOD FOR THE NONSTATIONARY NAVIER-STOKES EQUATIONS II: TIME DISCRETIZATION |
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摘 要: |
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关 键 词: | 有限元GALERKIN法 NAVIER-STOKES方程 偏微分方程 时间离散化 |
A Two-Level Finite Element Galerkin Method for the Nonstationary Navier-Stokes Equations II: Time Discretization |
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Authors: | Yinnian He Huanling Miao & Chunfeng Ren |
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Abstract: | In this article we consider the fully discrete two-level finite element Galerkin method for the two-dimensional nonstationary incompressible Navier-Stokes equations. This method consists in dealing with the fully discrete nonlinear Navier-Stokes problem on a coarse mesh with width $H$ and the fully discrete linear generalized Stokes problem on a fine mesh with width $h << H$. Our results show that if we choose $H=O(h^{1/2}$) this method is as the same stability and convergence as the fully discrete standard finite element Galerkin method which needs dealing with the fully discrete nonlinear Navier-Stokes problem on a fine mesh with width $h$. However, our method is cheaper than the standard fully discrete finite element Galerkin method. |
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Keywords: | Navier-Stokes equations Galerkin method Finite element |
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