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 | |
| Publication status | Published - 2004 |
| Externally published | Yes |
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Keywords
- Computer assisted proof
- Fixed-point theorem
- Rayleigh-Bénard convection
ASJC Scopus subject areas
- Mathematical Physics
- Condensed Matter Physics
- Computational Mathematics
- Applied Mathematics
Cite this
A numerical verification of nontrivial solutions for the heat convection problem. / Watanabe, Yoshitaka; Yamamoto, Nobito; Nakao, Mitsuhiro T.; Nishida, Takaaki.
In: Journal of Mathematical Fluid Mechanics, Vol. 6, No. 1, 2004, p. 1-20.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A numerical verification of nontrivial solutions for the heat convection problem
AU - Watanabe, Yoshitaka
AU - Yamamoto, Nobito
AU - Nakao, Mitsuhiro T.
AU - Nishida, Takaaki
PY - 2004
Y1 - 2004
N2 - 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.
AB - 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.
KW - Computer assisted proof
KW - Fixed-point theorem
KW - Rayleigh-Bénard convection
UR - http://www.scopus.com/inward/record.url?scp=10044237618&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=10044237618&partnerID=8YFLogxK
U2 - 10.1007/s00021-003-0077-3
DO - 10.1007/s00021-003-0077-3
M3 - Article
VL - 6
SP - 1
EP - 20
JO - Journal of Mathematical Fluid Mechanics
JF - Journal of Mathematical Fluid Mechanics
SN - 1422-6928
IS - 1
ER -