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

Fingerprint

Numerical Verification
Elliptic Operator
Verify
Eigenvalue
Sobolev spaces
Schauder Fixed Point Theorem
Eigenvalues and Eigenfunctions
Finite Element Solution
Numerical Techniques
Solution Set
Absolute value
Eigenvalues and eigenfunctions
Sobolev Spaces
Error Estimates
Numerical Examples
Approximation
Operator

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Numerical Verifications for Eigenvalues of Second-Order Elliptic Operators. / Nakao, M. T.; Yamamoto, N.; Nagatou, K.

In: Japan Journal of Industrial and Applied Mathematics, Vol. 16, No. 3, 10.1999, p. 307-320.

Research output: Contribution to journalArticle

Nakao, M. T. ; Yamamoto, N. ; Nagatou, K. / Numerical Verifications for Eigenvalues of Second-Order Elliptic Operators. In: Japan Journal of Industrial and Applied Mathematics. 1999 ; Vol. 16, No. 3. pp. 307-320.
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