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

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1 Citation (Scopus)

Abstract

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).

Original languageEnglish
Pages (from-to)157-170
Number of pages14
JournalJournal of Computational and Applied Mathematics
Volume302
DOIs
Publication statusPublished - Aug 15 2016

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Computer-assisted Proof
Numerical Verification
Rounding error
Floating point
Steady-state Solution
Nontrivial Solution
Viscous Fluid
Incompressible Fluid
Continuation
Fixed point theorem
Mathematical operators
Numerical Results
Fluids
Operator

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics

Cite this

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abstract = "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).",
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