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 journalArticlepeer-review

    6 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 - Mar 2015

    All Science Journal Classification (ASJC) codes

    • Engineering(all)
    • Applied Mathematics

    Fingerprint Dive into the research topics of 'Some considerations of the invertibility verifications for linear elliptic operators'. Together they form a unique fingerprint.

    Cite this