论文信息 - A Numerical Verification of Nontrivial Solutions for the Heat Convection Problem

A Numerical Verification of Nontrivial Solutions for the Heat Convection Problem

AbstractA computer assisted proof of the existence of nontrivial steady-state solutions for the two-dimensional Rayleigh-Bénard convection is described. The method is based on an infinite dimensional fixed-point theorem using a Newton-like operator. This paper also proposes a numerical verification algorithm which generates automatically on a computer a set including the exact nontrivial solution. All discussed numerical examples take into account of the effects of rounding errors in the floating point computations.

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