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October 2009 Numerical Verification Method of Solutions for Elliptic Equations and Its Application to the Rayleigh--Bénard Problem
Yoshitaka Watanabe, Mitsuhiro T. Nakao
Japan J. Indust. Appl. Math. 26(2-3): 443-463 (October 2009).

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.

Citation

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Yoshitaka Watanabe. Mitsuhiro T. Nakao. "Numerical Verification Method of Solutions for Elliptic Equations and Its Application to the Rayleigh--Bénard Problem." Japan J. Indust. Appl. Math. 26 (2-3) 443 - 463, October 2009.

Information

Published: October 2009
First available in Project Euclid: 1 February 2010

zbMATH: 1184.65106
MathSciNet: MR2589484

Rights: Copyright © 2009 The Japan Society for Industrial and Applied Mathematics

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Vol.26 • No. 2-3 • October 2009
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