Abstract
A 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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Watanabe, Y., Yamamoto, N., Nakao, M.T. et al. A Numerical Verification of Nontrivial Solutions for the Heat Convection Problem . J. math. fluid mech. 6, 1–20 (2004). https://doi.org/10.1007/s00021-003-0077-3
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DOI: https://doi.org/10.1007/s00021-003-0077-3