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Numerical verification method of solutions for elliptic equations and its application to the Rayleigh-Bénard problem. (English) Zbl 1184.65106

Summary: 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.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65C20 Probabilistic models, generic numerical methods in probability and statistics
35B32 Bifurcations in context of PDEs
35J66 Nonlinear boundary value problems for nonlinear elliptic equations
65N15 Error bounds for boundary value problems involving PDEs

Software:

PROFIL/BIAS

References:

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