Spectral analysis and numerical simulation for second order elliptic operator with highly oscillating coefficients in perforated domains with a periodic structure

This paper discusses the spectral properties and numerical simulation for the second order elliptic operators with rapidly oscillating coefficients in the domains which may contain small cavities distributed periodically with period ε. A multiscale asymptotic analysis formula for this problem is obtained by constructing properly the boundary layer. Finally, numerical results are given, which provide a strong support for the analytical estimates