, Volume 26, Issue 2-3, pp 443-463

Numerical verification method of solutions for elliptic equations and its application to the Rayleigh-Bénard problem

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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.