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 language | English |
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Pages (from-to) | 443-463 |
Number of pages | 21 |
Journal | Japan Journal of Industrial and Applied Mathematics |
Volume | 26 |
Issue number | 2-3 |
Publication status | Published - 2009 Oct |
Externally published | Yes |
Keywords
- Bifurcation point
- Elliptic equations
- Numerical verification method
- Rayleigh-Bénard problem
ASJC Scopus subject areas
- Engineering(all)
- Applied Mathematics