Multiscale numerical algorithm for the elliptic eigenvalue problem with the mixed boundary in perforated domains Original Research Article

In this paper, we study the elliptic eigenvalue problem with the mixed boundary in a perforated domain. The higher-order asymptotic expansions of the eigenvalues and the eigenfunctions for the problem will be presented. We derive the rigorous justification of the convergence results. From this, a multiscale finite element method and some numerical examples are presented.