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

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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.

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Authors and Affiliations

  1. Institute of Computational Mathematics and Science-Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, P.O.Box 2719, Beijing, 100080, P.R.China

    Li-Qun Cao

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  1. Li-Qun Cao
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Correspondence to Li-Qun Cao.

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This work is Supported by National Natural Science Foundation of China (grant # 10372108, # 90405016), and Special Funds for Major State Basic Research Projects( grant # TG2000067102)

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Cao, LQ. Multiscale asymptotic expansion and finite element methods for the mixed boundary value problems of second order elliptic equation in perforated domains. Numer. Math. 103, 11–45 (2006). https://doi.org/10.1007/s00211-005-0668-4

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  • DOI: https://doi.org/10.1007/s00211-005-0668-4

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