A numerical method to verify the invertibility of linear elliptic operators with applications to nonlinear problems

M. T. Nakao, K. Hashimoto, Y. Watanabe

    Research output: Contribution to journalArticlepeer-review

    31 Citations (Scopus)

    Abstract

    In this paper, we propose a numerical method to verify the invertibility of second-order linear elliptic operators. By using the projection and the constructive a priori error estimates, the invertibility condition is formulated as a numerical inequality based upon the existing verification method originally developed by one of the authors. As a useful application of the result, we present a new verification method of solutions for nonlinear elliptic problems, which enables us to simplify the verification process. Several numerical examples that confirm the actual effectiveness of the method are presented.

    Original languageEnglish
    Pages (from-to)1-14
    Number of pages14
    JournalComputing (Vienna/New York)
    Volume75
    Issue number1 SPEC. ISS.
    DOIs
    Publication statusPublished - Jul 2005

    All Science Journal Classification (ASJC) codes

    • Software
    • Theoretical Computer Science
    • Numerical Analysis
    • Computer Science Applications
    • Computational Theory and Mathematics
    • Computational Mathematics

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