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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:
65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
65C20Models (numerical methods)
35B32Bifurcation (PDE)
35J66Nonlinear boundary value problems for nonlinear elliptic equations
65N15Error bounds (BVP of PDE)
Software:
PROFIL/BIAS
References:
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