Japan Journal of Industrial and Applied Mathematics

Numerical Verification Method of Solutions for Elliptic Equations and Its Application to the Rayleigh--Bénard Problem

Yoshitaka Watanabe and Mitsuhiro T. Nakao

Full-text: Open access

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.

Article information

Source
Japan J. Indust. Appl. Math., Volume 26, Number 2-3 (2009), 443-463.

Dates
First available in Project Euclid: 1 February 2010

Permanent link to this document
https://projecteuclid.org/euclid.jjiam/1265033790

Mathematical Reviews number (MathSciNet)
MR2589484

Zentralblatt MATH identifier
1184.65106

Keywords
numerical verification method elliptic equations Rayleigh--Bénard problem bifurcation point

Citation

Watanabe, Yoshitaka; Nakao, Mitsuhiro T. Numerical Verification Method of Solutions for Elliptic Equations and Its Application to the Rayleigh--Bénard Problem. Japan J. Indust. Appl. Math. 26 (2009), no. 2-3, 443--463. https://projecteuclid.org/euclid.jjiam/1265033790


Export citation