Local and parallel finite element algorithms based on two-grid discretization for steady Navier-Stokes equations  

作　　者：马飞遥 马逸尘 沃维丰 

机构地区：[1]College of Science, Xi'an Jiaotong University, Xi'an 710049, P. R. China [2]Center for Nonlinear Studies, Northwest University, Xi'an 710069, P. R. China

出　　处：《Applied Mathematics and Mechanics(English Edition)》2007年第1期27-35,共9页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China (No. 10371096)

摘　　要：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 droping the coarse solution of the region near the boundary. By overlapping domain decomposition, the parallel algorithms are obtained. This paper analyzes the error of these algorithms and gets some error estimates which are better than those 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 high efficient.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 droping the coarse solution of the region near the boundary. By overlapping domain decomposition, the parallel algorithms are obtained. This paper analyzes the error of these algorithms and gets some error estimates which are better than those 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 high efficient.

关 键 词：Navier-Stokes equations finite element method two-grid LOCAL PARALLEL 

分 类 号：O241.82[理学—计算数学]