| Navier-Stokes方程的一种并行两水平有限元方法 |
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| 引用本文： | 尚月强,罗振东. Navier-Stokes方程的一种并行两水平有限元方法[J]. 应用数学和力学, 2010, 31(11): 1351-1359. DOI: 10.3879/j.issn.1000-0887.2010.11.008 |
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| 作者姓名： | 尚月强 罗振东 |
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| 作者单位： | 贵州师范大学 数学与计算机科学学院,贵阳 550001; |
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| 基金项目： | 国家自然科学基金资助项目，贵州省科学技术基金资助项目 |
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| 摘 要： | 基于区域分解技巧,提出了一种求解定常Navier-Stokes方程的并行两水平有限元方法．该方法首先在一粗网格上求解Navier-Stokes方程,然后在细网格的子区域上并行求解粗网格解的残差方程,以校正粗网格解．该方法实现简单,通信需求少．使用有限元局部误差估计,推导了并行方法所得近似解的误差界,同时通过数值算例,验证了其高效性．
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| 关 键 词： | Navier-Stokes方程 有限元方法 两水平方法 重叠型区域分解 并行算法 |
| 收稿时间： | 1900-01-01 |
A Parallel Two-Level Finite Element Method for the Navier-Stokes Equations |
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| SHANG Yue-qiang,LUO Zhen-dong. A Parallel Two-Level Finite Element Method for the Navier-Stokes Equations[J]. Applied Mathematics and Mechanics, 2010, 31(11): 1351-1359. DOI: 10.3879/j.issn.1000-0887.2010.11.008 |
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| Authors: | SHANG Yue-qiang LUO Zhen-dong |
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| Affiliation: | School of Mathematics and Computer Science, Guizhou Normal University, Guiyang 550001, P. R. China;School of Mathematics and Physics, North China Electric Power University, Beijing 102206, P. R. China |
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| Abstract: | Based on domain decomposition,a parallel two-level finite element method for the stationary Navier-Stokes equations was proposed and analyzed. The basic idea of the method was to first solve the Navier-Stokes equations on a coarse grid,then to solve the resulted residual equations in parallel on a fine grid. This method has low communication complexity. It can be implemented easily. By local a priori error estimate for finite element discretizations,error bounds of the approximate solution were derived. Numerical results were also given to illustrate the high efficiency of the method. |
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