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 |
|---|---|
| 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 |
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Keywords
- Bifurcation point
- Elliptic equations
- Numerical verification method
- Rayleigh-Bénard problem
ASJC Scopus subject areas
- Engineering(all)
- Applied Mathematics
Cite this
Numerical verification method of solutions for elliptic equations and its application to the Rayleigh-Bénard problem. / Watanabe, Yoshitaka; Nakao, Mitsuhiro T.
In: Japan Journal of Industrial and Applied Mathematics, Vol. 26, No. 2-3, 10.2009, p. 443-463.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Numerical verification method of solutions for elliptic equations and its application to the Rayleigh-Bénard problem
AU - Watanabe, Yoshitaka
AU - Nakao, Mitsuhiro T.
PY - 2009/10
Y1 - 2009/10
N2 - 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.
AB - 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.
KW - Bifurcation point
KW - Elliptic equations
KW - Numerical verification method
KW - Rayleigh-Bénard problem
UR - http://www.scopus.com/inward/record.url?scp=77149138349&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=77149138349&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:77149138349
VL - 26
SP - 443
EP - 463
JO - Japan Journal of Industrial and Applied Mathematics
JF - Japan Journal of Industrial and Applied Mathematics
SN - 0916-7005
IS - 2-3
ER -