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.


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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