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

Yoshitaka Watanabe, Mitsuhiro T. Nakao

Research output: Contribution to journalArticle

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

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Numerical Verification
Rayleigh
Elliptic Equations
Heat convection
Bifurcation Point
Convection
Existence of Solutions
Heat
Verify
Three-dimensional

All Science Journal Classification (ASJC) codes

  • Engineering(all)
  • Applied Mathematics

Cite this

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