特征值问题的自适应反迭代有限元算法  

AN ADAPTIVE INVERSE ITERATION FINITE ELEMENT ALGORITHM FOR EIGENVALUE PROBLEMS

作　　者：袁健华[1] 

机构地区：[1]北京邮电大学理学院 北京 100876

出　　处：《高等学校计算数学学报》2008年第2期141-151,共11页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金(10701016)

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。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.

关 键 词：特征值问题 有限元算法 自适应 LIPSCHITZ SOBOLEV空间 有界闭区域 双线性泛函 迭代 

分 类 号：O241.6[理学—计算数学] TP391.41[理学—数学]