Computer assisted proofs of bifurcating solutions for nonlinear heat convection problems

Mitsuhiro T. Nakao, Yoshitaka Watanabe, Nobito Yamamoto, Takaaki Nishida, Myoung Nyoung Kim

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


In previous works (Nakao et al., Reliab. Comput., 9(5):359-372, 2003; Watanabe et al., J. Math. Fluid Mech., 6(1):1-20, 2004), the authors considered the numerical verification method of solutions for two-dimensional heat convection problems known as Rayleigh-Bénard problem. In the present paper, to make the arguments self-contained, we first summarize these results including the basic formulation of the problem with numerical examples. Next, we will give a method to verify the bifurcation point itself, which should be an important information to clarify the global bifurcation structure, and show a numerical example. Finally, an extension to the three dimensional case will be described.

Original languageEnglish
Pages (from-to)388-401
Number of pages14
JournalJournal of Scientific Computing
Issue number3
Publication statusPublished - 2010 Jun
Externally publishedYes


  • Bifurcation point
  • Computer assisted proof
  • Navier-Stokes equation
  • Nonlinear heat convection

ASJC Scopus subject areas

  • Software
  • Computational Theory and Mathematics
  • Theoretical Computer Science
  • Engineering(all)


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