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Convergence and optimal complexity of adaptive finite element eigenvalue computations

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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.

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Author information

Authors and Affiliations

  1. LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Xiaoying Dai & Aihui Zhou

  2. Graduate University of Chinese Academy of Sciences, Beijing, 100190, China

    Xiaoying Dai

  3. Center for Computational Mathematics and Applications, Department of Mathematics, Pennsylvania State University, University Park, PA, 16802, USA

    Jinchao Xu

Authors
  1. Xiaoying Dai
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  2. Jinchao Xu
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  3. Aihui Zhou
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Corresponding author

Correspondence to Jinchao Xu.

Additional information

This work was partially supported by the National Science Foundation of China under grant 10425105 and the National Basic Research Program under grant 2005CB321704.

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Dai, X., Xu, J. & Zhou, A. Convergence and optimal complexity of adaptive finite element eigenvalue computations. Numer. Math. 110, 313–355 (2008). https://doi.org/10.1007/s00211-008-0169-3

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  • DOI: https://doi.org/10.1007/s00211-008-0169-3

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