Some considerations of the invertibility verifications for linear elliptic operators

Mitsuhiro T. Nakao, Yoshitaka Watanabe, Takehiko Kinoshita, Takuma Kimura, Nobito Yamamoto

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

This paper presents three computer-assisted procedures for verifying the invertibility of second-order linear elliptic operators and for computing a bound on the norm of its inverse. One of these procedures is an improvement of a theorem by Nakao et al. (Computing 75:1–14, 2005) that uses projection and constructive a priori error estimates and was proposed by two of the authors of this paper. Results verifying these procedures are presented for several numerical examples.

Original languageEnglish
Pages (from-to)19-31
Number of pages13
JournalJapan Journal of Industrial and Applied Mathematics
Volume32
Issue number1
DOIs
Publication statusPublished - 2015
Externally publishedYes

Fingerprint

Invertibility
Elliptic Operator
Linear Operator
A Priori Error Estimates
Computing
Projection
Norm
Numerical Examples
Theorem

Keywords

  • Computer-assisted proof
  • Differential operators
  • Numerical verification
  • Solvability of linear problem

ASJC Scopus subject areas

  • Applied Mathematics
  • Engineering(all)

Cite this

Some considerations of the invertibility verifications for linear elliptic operators. / Nakao, Mitsuhiro T.; Watanabe, Yoshitaka; Kinoshita, Takehiko; Kimura, Takuma; Yamamoto, Nobito.

In: Japan Journal of Industrial and Applied Mathematics, Vol. 32, No. 1, 2015, p. 19-31.

Research output: Contribution to journalArticle

Nakao, Mitsuhiro T. ; Watanabe, Yoshitaka ; Kinoshita, Takehiko ; Kimura, Takuma ; Yamamoto, Nobito. / Some considerations of the invertibility verifications for linear elliptic operators. In: Japan Journal of Industrial and Applied Mathematics. 2015 ; Vol. 32, No. 1. pp. 19-31.
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