特征值问题有限元逼近位移超收敛的一个定理

A THEOREM ON SUPERCONVERGENCE OF THE FINITE ELEMENT APPROXIMATIONS FOR EIGENVALUE PROBLEMS

本文建立了二阶椭圆特征值问题 m 次有限元逼近位移超收敛定理:‖Pu-u_h‖_(0,∞)≤ch^(m+2),m≥2‖Pu-u_h‖_(0,∞)≤ch^(m+1+(2/ξ),m≥3其中,1<ξ<2,u_h 是 m 次有限元特征函数,u 是某一精确特征函数,P 是 Ritz 投影算子。利用这个定理就可以把二阶线性椭圆方程有限元逼近位移超收敛的结果移植到特征值问题,

In this paper,the superconvergence results of “shift” of the finite eleme-nt approximations for linear 2th order alliptic differential equation are gene-ralized to the cases of eigenvalue problem.