中文摘要：

1 引言 设Ω∈R^2己。为Lipschitz单连通的有界闭区域，X为定义在Ω的Sobolev空间，a（．，．）和b（.，.）为X×X→C的有界双线性或半双线性泛函，考虑变分特征值问题：求（λ，u≠0）∈C×X使得

英文摘要：

In this paper, an adaptive finite element method is proposed to compute eigenvalue problems. The adaptive finite element methods based on the a posterior error estimates are known to be successful in resolving singularities of eigenfunctions which deteriorate the finite element convergence. Comparing with existing adaptive methods, the adaptive inverse iteration finite element algorithm for eigenvalue problems can use the a posterior error estimators of normal variational problems. Numerical results are reported to illustrate the quasi-optimal performance of the adaptive inverse iteration finite element algorithm.