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

Abstract

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.