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)


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
Issue number2-3
Publication statusPublished - 2009 Oct
Externally publishedYes



  • Bifurcation point
  • Elliptic equations
  • Numerical verification method
  • Rayleigh-Bénard problem

ASJC Scopus subject areas

  • Engineering(all)
  • Applied Mathematics

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