Japan Journal of Industrial and Applied Mathematics
- Japan J. Indust. Appl. Math.
- Volume 26, Number 2-3 (2009), 443-463.
Numerical Verification Method of Solutions for Elliptic Equations and Its Application to the Rayleigh--Bénard Problem
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.
Japan J. Indust. Appl. Math., Volume 26, Number 2-3 (2009), 443-463.
First available in Project Euclid: 1 February 2010
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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