An efficient numerical verification method for the Kolmogorov problem of incompressible viscous fluid

Some computer-assisted proofs of nontrivial steady-state solutions for the Kolmogorov flows are presented. The method is based on the infinite-dimensional fixed-point theorem using a Newton-like operator with a numerical verification algorithm that automatically generates a set that includes the exa...

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Bibliographic Details
Published inJournal of computational and applied mathematics Vol. 302; pp. 157 - 170
Main Author Watanabe, Yoshitaka
Format Journal Article
LanguageEnglish
Published Elsevier B.V 15.08.2016
Subjects
Algorithms
Computation
Computational fluid dynamics
Computer-assisted proof
Fixed-point theorem
Floating point arithmetic
Fluid flow
Incompressible flow
Kolmogorov flows
Mathematical models
Theorem proving
76D03
65N15
35Q30
Computer-assisted proof
Fixed-point theorem
Kolmogorov flows
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Summary:Some computer-assisted proofs of nontrivial steady-state solutions for the Kolmogorov flows are presented. The method is based on the infinite-dimensional fixed-point theorem using a Newton-like operator with a numerical verification algorithm that automatically generates a set that includes the exact nontrivial solution. When discussing the numerical results, we consider the effects of rounding errors in the floating point computations. This is a continuation of our study that was presented in Watanabe (2009).
Bibliography:ObjectType-Article-1
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ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2016.01.055