TY - JOUR
T1 - An efficient numerical verification method for the Kolmogorov problem of incompressible viscous fluid
AU - Watanabe, Yoshitaka
N1 - Funding Information:
We would like to thank the referees for many helpful insights and comments. This work was supported by a Grant-in-Aid from the Ministry of Education, Culture, Sports, Science and Technology of Japan (Nos. 24340018 , 15H03637 ). Most of the computations were carried out using the computer facilities at the Research Institute for Information Technology, Kyushu University.
Publisher Copyright:
© 2016 Elsevier B.V. All rights reserved.
PY - 2016/8/15
Y1 - 2016/8/15
N2 - 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).
AB - 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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U2 - 10.1016/j.cam.2016.01.055
DO - 10.1016/j.cam.2016.01.055
M3 - Article
AN - SCOPUS:84959358640
SN - 0377-0427
VL - 302
SP - 157
EP - 170
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
ER -