### 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.

Original language | English |
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Pages (from-to) | 1-20 |

Number of pages | 20 |

Journal | Journal of Mathematical Fluid Mechanics |

Volume | 6 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2004 |

Externally published | Yes |

### Keywords

- Computer assisted proof
- Fixed-point theorem
- Rayleigh-Bénard convection

### ASJC Scopus subject areas

- Mathematical Physics
- Condensed Matter Physics
- Computational Mathematics
- Applied Mathematics

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## Cite this

Watanabe, Y., Yamamoto, N., Nakao, M. T., & Nishida, T. (2004). A numerical verification of nontrivial solutions for the heat convection problem.

*Journal of Mathematical Fluid Mechanics*,*6*(1), 1-20. https://doi.org/10.1007/s00021-003-0077-3