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

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:302

Article

Watanabe, Yoshitaka^1,2 

[1] Kyushu Univ, Res Inst Informat Technol, Higashi Ku, 6-10-1 Hakozaki, Fukuoka 8128518, Japan

[2] Japan Sci & Technol Agcy, CREST, Tokyo, Japan

关键词: Kolmogorov flows;    Computer-assisted proof;    Fixed-point theorem;   

DOI  :  10.1016/j.cam.2016.01.055

来源: Elsevier

【 摘 要 】

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). (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free