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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. (English) Zbl 1049.65126
Authors’ summary: 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 multiscale finite element algorithms and numerical results are proposed.

MSC:
65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs
35P15 Estimates of eigenvalues in context of PDEs
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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