Two-level stabilized finite element method for Stokes eigenvalue problem  

作　　者：黄鹏展 何银年 冯新龙 

机构地区：[1]College of Mathematics and System Sciences,Xinjiang University [2]Center for Computational Geoscienes,School of Mathematics and Statistics,Xi'an Jiaotong University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2012年第5期621-630,共10页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Nos.10901131,10971166, and 10961024);the National High Technology Research and Development Program of China (No.2009AA01A135);the Natural Science Foundation of Xinjiang Uygur Autonomous Region (No.2010211B04)

摘　　要：A two-level stabilized finite element method for the Stokes eigenvalue problem based on the local Gauss integration is considered. This method involves solving a Stokes eigenvalue problem on a coarse mesh with mesh size H and a Stokes problem on a fine mesh with mesh size h -- O（H2）, which can still maintain the asymptotically optimal accuracy. It provides an approximate solution with the convergence rate of the same order as the usual stabilized finite element solution, which involves solving a Stokes eigenvalue problem on a fine mesh with mesh size h. Hence, the two-level stabilized finite element method can save a large amount of computational time. Moreover, numerical tests confirm the theoretical results of the present method.A two-level stabilized finite element method for the Stokes eigenvalue problem based on the local Gauss integration is considered. This method involves solving a Stokes eigenvalue problem on a coarse mesh with mesh size H and a Stokes problem on a fine mesh with mesh size h -- O（H2）, which can still maintain the asymptotically optimal accuracy. It provides an approximate solution with the convergence rate of the same order as the usual stabilized finite element solution, which involves solving a Stokes eigenvalue problem on a fine mesh with mesh size h. Hence, the two-level stabilized finite element method can save a large amount of computational time. Moreover, numerical tests confirm the theoretical results of the present method.

关 键 词：Stokes eigenvalue problem stabilized method lowest equal-order pair two-level method 

分 类 号：O241.82[理学—计算数学]