Local and Parallel Finite Element Algorithms Based on Two-Grid Discretization for Steady Navier-Stokes Equations
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摘要: 对二维定常的不可压缩的Navier-Stokes方程的局部和并行算法进行了研究．给出的算法是多重网格和区域分解相结合的算法，它是基于两个有限元空间：粗网格上的函数空间和子区域的细网格上的函数空间．局部算法是在粗网格上求一个非线性问题，然后在细网格上求一个线性问题，并舍掉内部边界附近的误差相对较大的解．最后，基于局部算法，通过有重叠的区域分解而构造了并行算法，并且做了算法的误差分析，得到了比标准有限元方法更好的误差估计，也对算法做了数值试验，数值结果通过比较验证了本算法的高效性和合理性．
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关键词:
- Navier-Stokes方程 /
- 有限元 /
- 二重网格 /
- 局部 /
- 并行
Abstract: Local and parallel finite element algorithms based on two-grid discretization for Navier-Stokes equations in two dimension are presented. Its basis is a coarse finite element space on the global domain and a fine finite element space on the subdomain. The local algorithm consists of finding a solution for a given nonlinear problem in the coarse finite element space and a solution for a linear problem in the fine finite element space, then it drops the coarse solution of the region near the boundary. At last, by overlapping domain decomposition, the parallel algorithms are obtained. The error of these algorithms are analyzed and some error estimates are got which are better than that of the standard finite element method. The numerical experiments are given too. By analyzing and comparing these results, it is shown that these algorithms are correct and highly efficient.-
Key words:
- Navier-Stokes equation /
- finite element method /
- two-grid /
- local /
- parallel
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