A numerical verification of nontrivial solutions for the heat convection problem

Yoshitaka Watanabe; Nobito Yamamoto; Mitsuhiro T. Nakao; Takaaki Nishida

doi:10.1007/s00021-003-0077-3

A numerical verification of nontrivial solutions for the heat convection problem

Yoshitaka Watanabe^*, Nobito Yamamoto, Mitsuhiro T. Nakao, Takaaki Nishida

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

17 Citations (Scopus)

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
Pages (from-to)	1-20
Number of pages	20
Journal	Journal of Mathematical Fluid Mechanics
Volume	6
Issue number	1
DOIs	https://doi.org/10.1007/s00021-003-0077-3
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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10.1007/s00021-003-0077-3

Cite this

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A numerical verification of nontrivial solutions for the heat convection problem

Abstract

Keywords

ASJC Scopus subject areas

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