| A NEW APPROXIMATE INERTIAL MANIFOLD AND ASSOCIATED ALGORITHM |
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| 作者姓名： | 李开泰 徐忠锋 杨晓忠 |
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| 作者单位： | Department of Mathematics Xi'an Jiaotong University，Department of Mathematics Xi'an Jiaotong University，Department of Mathematics North China Electric Power University Xi'an 710049，China，Xi'an 710049，China，Zhengzhou 450045，China |
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| 基金项目： | Subsidized by the Special Funds for Major State Basic Research Projects (G1999 03 2801)
NFS of China (10001028 and 40375010) |
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| 摘 要： | In this article the authors propose a new approximate inertial manifold(AIM) to the Navier-Stokes equations. The solutions are in the neighborhoods of this AIM with thickness δ=o(h2k 1-ε). The article aims to investigate a two grids finite element approximation based on it and give error estimates of the approximate solution where (h, h*) and (k, m) are coarse and fine meshes and degree of finite element subspaces, respectively. These results are much better than Standard Galerkin(SG) and nonlinear Galerkin (NG) methods. For example, for 2D NS eqs and linear element, let uh,uh,u* be the SG, NG and their approximate solutions respectively, then and h*≈h2 for NG, h*≈h3/2 for theirs.
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| 关 键 词： | 惯性流形 联合算法 有限元分析 Navier-Stokes方程 |
| 收稿时间： | 2003-01-02 |
A NEW APPROXIMATE INERTIAL MANIFOLD AND ASSOCIATED ALGORITHM |
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| Li Kaitai,Xu Zhongfeng,Yang Xiaozhong.A NEW APPROXIMATE INERTIAL MANIFOLD AND ASSOCIATED ALGORITHM[J].Acta Mathematica Scientia,2006,26(1):1-16. |
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| Authors: | Li Kaitai Xu Zhongfeng Yang Xiaozhong |
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| Abstract: | |
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| Keywords: | Two level finite element Navier-Stokes equations new approximation inertial manifold |
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