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

Li Qun Cao; Jian Lan Luo

doi:10.1016/j.apnum.2007.07.009

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

Li Qun Cao^*
, Jian Lan Luo

^*Corresponding author for this work

School of Physics

CAS - Academy of Mathematics and System Sciences

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

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.

Original language	English
Pages (from-to)	1349-1374
Number of pages	26
Journal	Applied Numerical Mathematics
Volume	58
Issue number	9
DOIs	https://doi.org/10.1016/j.apnum.2007.07.009
State	Published - Sep 2008

Keywords

Asymptotic expansion
Elliptic eigenvalue problem
Finite element method
Homogenization
Perforated domain

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10.1016/j.apnum.2007.07.009

Cite this

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title = "Multiscale numerical algorithm for the elliptic eigenvalue problem with the mixed boundary in perforated domains",

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.",

keywords = "Asymptotic expansion, Elliptic eigenvalue problem, Finite element method, Homogenization, Perforated domain",

author = "Cao, \{Li Qun\} and Luo, \{Jian Lan\}",

year = "2008",

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AU - Luo, Jian Lan

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AB - 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.

KW - Asymptotic expansion

KW - Elliptic eigenvalue problem

KW - Finite element method

KW - Homogenization

KW - Perforated domain

UR - https://www.scopus.com/pages/publications/48349108967

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DO - 10.1016/j.apnum.2007.07.009

M3 - 文章

AN - SCOPUS:48349108967

SN - 0168-9274

VL - 58

SP - 1349

EP - 1374

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

IS - 9

ER -

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

Abstract

Keywords

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