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 journalArticlepeer-review

    3 Citations (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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