Numerical verifications of solutions for nonlinear elliptic equations

Yoshitaka Watanabe, Mitsuhiro T. Nakao

    Research output: Contribution to journalArticlepeer-review

    26 Citations (Scopus)


    A numerical technique which enables us to verify the existence of weak solutions for nonlinear elliptic boundary value problems is proposed. It is based on the infinite dimensional fixed point theorems using the Newton-like operator and the error estimates for finite element approximations. We also present an effective verification procedure which automatically generates the set including the exact solution in a computer. Some numerical examples are illustrated.

    Original languageEnglish
    Pages (from-to)165-178
    Number of pages14
    JournalJapan Journal of Industrial and Applied Mathematics
    Issue number1
    Publication statusPublished - Feb 1993

    All Science Journal Classification (ASJC) codes

    • Engineering(all)
    • Applied Mathematics


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