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A Numerical Verification of Nontrivial Solutions for the Heat Convection Problem

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Journal of Mathematical Fluid Mechanics Aims and scope Submit manuscript

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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Authors and Affiliations

  1. Computing and Communications Center, Kyushu University, 812-8581, Fukuoka, Japan

    Yoshitaka Watanabe

  2. Department of Computer Science and Information Mathematics, The University of Electro-Communications, 182-8585, Chofu, Japan

    Nobito Yamamoto

  3. Graduate School of Mathematics, Kyushu University, 812-8581, Fukuoka, Japan

    Mitsuhiro T. Nakao

  4. Graduate School of Science, Kyoto University, 606-8502, Kyoto, Japan

    Takaaki Nishida

Authors
  1. Yoshitaka Watanabe
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  2. Nobito Yamamoto
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  3. Mitsuhiro T. Nakao
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  4. Takaaki Nishida
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Correspondence to Yoshitaka Watanabe.

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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

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