An improved method for verifying the existence and bounds of the inverse of second-order linear elliptic operators mapping to dual space

Yoshitaka Watanabe, Takehiko Kinoshita, Mitsuhiro T. Nakao

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

This paper presents an improved method for determining the invertibility of second-order linear elliptic operators with a bound on the norm of their inverses by computers in a mathematically rigorous sense. This approach is an improvement on a previous method (Nakao et al. in Jpn J Ind Appl Math 32:19–32, 2015) which used a projection and constructive a priori error estimates. Several examples confirming the effectiveness of the proposed procedure are reported.

Original languageEnglish
Pages (from-to)407-420
Number of pages14
JournalJapan Journal of Industrial and Applied Mathematics
Volume36
Issue number2
DOIs
Publication statusPublished - Jul 1 2019

All Science Journal Classification (ASJC) codes

  • Engineering(all)
  • Applied Mathematics

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