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
Publication statusPublished - 2009 Oct
Externally publishedYes

Fingerprint

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

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 journalArticle

@article{2b226920f1cd40aebfe58d93815ecb4e,
title = "Numerical verification method of solutions for elliptic equations and its application to the Rayleigh-B{\'e}nard problem",
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-B{\'e}nard 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.",
keywords = "Bifurcation point, Elliptic equations, Numerical verification method, Rayleigh-B{\'e}nard problem",
author = "Yoshitaka Watanabe and Nakao, {Mitsuhiro T.}",
year = "2009",
month = "10",
language = "English",
volume = "26",
pages = "443--463",
journal = "Japan Journal of Industrial and Applied Mathematics",
issn = "0916-7005",
publisher = "Springer Japan",
number = "2-3",

}

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 -