Some considerations of the invertibility verifications for linear elliptic operators

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


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
Issue number1
Publication statusPublished - 2015
Externally publishedYes


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

ASJC Scopus subject areas

  • Applied Mathematics
  • Engineering(all)


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