Article

Numerische Mathematik

, Volume 110, Issue 3, pp 313-355

First online:

Convergence and optimal complexity of adaptive finite element eigenvalue computations

  • Xiaoying DaiAffiliated withLSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of SciencesGraduate University of Chinese Academy of Sciences
  • , Jinchao XuAffiliated withCenter for Computational Mathematics and Applications, Department of Mathematics, Pennsylvania State University Email author 
  • , Aihui ZhouAffiliated withLSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

Abstract

In this paper, an adaptive finite element method for elliptic eigenvalue problems is studied. Both uniform convergence and optimal complexity of the adaptive finite element eigenvalue approximation are proved. The analysis is based on a certain relationship between the finite element eigenvalue approximation and the associated finite element boundary value approximation which is also established in the paper.

Mathematics Subject Classification (2000)

65F15 65N15 65N25 65N30 65N50