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Asymptotic expansions and numerical algorithms of eigenvalues and eigenfunctions of the Dirichlet problem for second order elliptic equations in perforated domains

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In this paper, we study the spectral properties of Dirichlet problems for second order elliptic equation with rapidly oscillating coefficients in a perforated domain. The asymptotic expansions of eigenvalues and eigenfunctions for this kind of problem are obtained, and the multiscale finite element algorithms and numerical results are proposed.

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Authors and Affiliations

  1. Institute of Computational Mathematics and Science-Engineering Computing, The Academy of Mathematics and System Sciences, The Chinese Academy of Sciences, P.O.Box 2719, Beijing, 100080, P.R.China

    Li-Qun Cao

  2. Institute of Computational Mathematics and Science-Engineering Computing, The Academy of Mathematics and System Sciences, The Chinese Academy of Sciences, P.O.Box 2719, Beijing, 100080, P.R.China

    Jun-Zhi Cui

Authors
  1. Li-Qun Cao
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  2. Jun-Zhi Cui
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Correspondence to Li-Qun Cao.

Additional information

Mathematics Subject Classification (2000): 65F10, 35P15

This work is Supported by National Natural Science Foundation of China (grant # 19932030) and Special Funds for Major State Basic Research Projects (grant # TG2000067102)

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Cao, LQ., Cui, JZ. Asymptotic expansions and numerical algorithms of eigenvalues and eigenfunctions of the Dirichlet problem for second order elliptic equations in perforated domains. Numer. Math. 96, 525–581 (2004). https://doi.org/10.1007/s00211-003-0468-7

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  • DOI: https://doi.org/10.1007/s00211-003-0468-7

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