解Stokes特征值问题的一种两水平稳定化有限元方法

A Two-Level Stabilized Finite Element Method for the Stokes Eigenvalue Problem

基于局部Gauss积分,研究了解Stokes特征值问题的一种两水平稳定化有限元方法.该方法涉及在网格步长为H的粗网格上解一个Stokes特征值问题,在网格步长为h=O(H2)的细网格上解一个Stokes问题.这样使其能够仍旧保持最优的逼近精度,求得的解和一般的稳定化有限元解具有相同的收敛阶,即直接在网格步长为h的细网格上解一个Stokes特征值问题.因此,该方法能够节省大量的计算时间.数值试验验证了理论结果.

A two-level stabilized finite element method for the Stokes eigenvalue problem based on local Gauss integration was considered.The method involved 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 an asymptotically optimal accuracy.The given method provided an approximate solution with the convergence rate of the same order as the usual stabilized finite element solution,which involved solving a Stokes eigenvalue problem on a fine mesh with mesh size h.Hence,the method can save a large amount of computational time.Moreover,numerical tests confirmed the theoretical results of the presented method.