Numerical verification method of solutions for elliptic equations and its application to the Rayleigh-Bénard problem

Yoshitaka Watanabe, Mitsuhiro T. Nakao

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    1 Citation (Scopus)

    Abstract

    We first summarize the general concept of our verification method of solutions for elliptic equations. Next, as an application of our method, a survey and future works on the numerical verification method of solutions for heat convection problems known as Rayleigh-Bénard problem are described. We will give a method to verify the existence of bifurcating solutions of the two-dimensional problem and the bifurcation point itself. Finally, an extension to the three-dimensional case and future works will be described.

    Original languageEnglish
    Pages (from-to)443-463
    Number of pages21
    JournalJapan Journal of Industrial and Applied Mathematics
    Volume26
    Issue number2-3
    DOIs
    Publication statusPublished - Oct 2009

    All Science Journal Classification (ASJC) codes

    • Engineering(all)
    • Applied Mathematics

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