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

Authors:
Li-Qun Cao;Jian-Lan Luo
Affiliations:
State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Science-Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy ...;Department of Applied Physics, Beijing University of Aeronautics and Astronautics, Beijing 100083, China
Venue:
Applied Numerical Mathematics
Year:
2008

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Abstract

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.