Multiscale asymptotic expansion and finite element methods for the mixed boundary value problems of second order elliptic equation in perforated domains

Authors:
Li-Qun Cao
Affiliations:
Institute of Computational Mathematics and Science-Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, P.O.Box 2719, 100080, Beijing, P.R.China
Venue:
Numerische Mathematik
Year:
2006

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Abstract

In this paper, we will discuss the mixed boundary value problems for the second order elliptic equation with rapidly oscillating coefficients in perforated domains, and will present the higher-order multiscale asymptotic expansion of the solution for the problem, which will play an important role in the numerical computation . The convergence theorems and their rigorous proofs will be given. Finally a multiscale finite element method and some numerical results will be presented.