Numerical Verifications for Eigenvalues of Second-Order Elliptic Operators

M. T. Nakao, N. Yamamoto, K. Nagatou

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

In this paper, we consider a numerical technique to verify the exact eigenvalues and eigenfunctions of second-order elliptic operators in some neighborhood of their approximations. This technique is based on Nakao's method [9] using the Newton-like operator and the error estimates for the C0 finite element solution. We construct, in computer, a set containing solutions which satisfies the hypothesis of Schauder's fixed point theorem for compact map on a certain Sobolev space. Moreover, we propose a method to verify the eigenvalue which has the smallest absolute value. A numerical example is presented.

Original languageEnglish
Pages (from-to)307-320
Number of pages14
JournalJapan Journal of Industrial and Applied Mathematics
Volume16
Issue number3
Publication statusPublished - 1999 Oct
Externally publishedYes

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Keywords

  • Eigenvalue problem
  • Elliptic operators
  • Error estimates
  • Finite element solution

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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