Convergence rates of eigenvalue problems in perforated domains: the case of small volume

This paper is concerned with the Dirichlet eigenvalue problem for Laplace operator in a bounded domain with periodic perforation in the case of small volume. We obtain the optimal quantitative error estimates independent of the spectral gaps for an asymptotic expansion, with two leading terms, of Di...

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Bibliographic Details
Published in:arXiv.org 2024-08
Main Authors: Shen, Zhongwei, Zhuge, Jinping
Format: Article
Language:English
Subjects:
Asymptotic series
Convergence
Eigenvalues
Eigenvectors
Error analysis
Laplace transforms
Quantitative analysis
Online Access:Get full text
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Summary:This paper is concerned with the Dirichlet eigenvalue problem for Laplace operator in a bounded domain with periodic perforation in the case of small volume. We obtain the optimal quantitative error estimates independent of the spectral gaps for an asymptotic expansion, with two leading terms, of Dirichlet eigenvalues. We also establish the convergence rates for the corresponding eigenfunctions. Our approach uses a known reduction to a degenerate elliptic eigenvalue problem for which a quantitative analysis is carried out.
ISSN:2331-8422