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

研究成果: Contribution to journal › Article › 査読

17 被引用数 (Scopus)

抄録

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.

本文言語	英語
ページ（範囲）	1-20
ページ数	20
ジャーナル	Journal of Mathematical Fluid Mechanics
巻	6
号	1
DOI	https://doi.org/10.1007/s00021-003-0077-3
出版ステータス	出版済み - 12 1 2004

All Science Journal Classification (ASJC) codes

数理物理学
凝縮系物理学
計算数学
応用数学

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10.1007/s00021-003-0077-3

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A numerical verification of nontrivial solutions for the heat convection problem

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