A numerical verification of nontrivial solutions for the heat convection problem
type: Item
instance of: scholarly article
title: A numerical verification of nontrivial solutions for the heat convection problem
zbMATH Open document ID: 1062.35092
author: Yoshitaka Watanabe
author: Nobito Yamamoto
author: Mitsuhiro T. Nakao
author: Takaaki Nishida
published in: Journal of Mathematical Fluid Mechanics
publication date: 2004-05-27T00:00:00Z
review text: The authors study two-dimensional Rayleigh-Bénard convection in Oberbeck-Boussinesq approximation. The solution is represented in double Fourier series, and then an infinite-dimen\-sional fixed-point formulation is introduced. The solution is constructed by iteration using a Newton-like operator and some a priori error estimates obtained for linearized problems. This paper also proposes a computer verification algorithm which generates automatically a set including the exact nontrivial solution. The method is illustrated by computing the first and second bifurcated solutions from the trivial solution. Numerical examples take into account rounding errors in the floating point computations.
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 35-04
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 76R10
Mathematics Subject Classification ID: 80A20
zbMATH DE Number: 2067265
zbMATH Keywords: Rayleigh-Benard convection
zbMATH Keywords: Oberbeck-Boussinesq approximation
zbMATH Keywords: fixed-point formulation
zbMATH Keywords: iteration
describes a project that uses: INTLIB
MaRDI profile type: Publication
full work available at URL: s00021-003-0077-3
OpenAlex ID: W1991606206
DOI: 10.1007/S00021-003-0077-3
description: scientific article; zbMATH DE number 2067265