TY - JOUR
T1 - Computer-assisted proof for the stationary solution existence of the Navier–Stokes equation over 3D domains
AU - Liu, Xuefeng
AU - Nakao, Mitsuhiro T.
AU - Oishi, Shin'ichi
N1 - Funding Information:
The first author is supported by Japan Society for the Promotion of Science: Fund for the Promotion of Joint International Research (Fostering Joint International Research (A)) 20KK0306 , Grant-in-Aid for Scientific Research, Japan (B) 20H01820 , 21H00998 , and Grant-in-Aid for Scientific Research, Japan (C) 18K03411 . The second author is supported by Grant-in-Aid for Scientific Research, Japan (C) 18K03434 , 21K03378 . The last author is supported by JST CREST, Japan Grant Number JPMJCR14D4 , Japan.
Publisher Copyright:
© 2021 Elsevier B.V.
PY - 2022/5
Y1 - 2022/5
N2 - This paper proposes a computer-assisted solution existence verification method for the stationary Navier–Stokes equation over general 3D domains. The proposed method verifies that the exact solution as the fixed point of the Newton iteration exists around the approximate solution through rigorous computation and error estimation. The explicit values of quantities required by applying the fixed-point theorem are obtained by utilizing newly developed quantitative error estimation for finite element solutions to boundary value problems and eigenvalue problems of the Stokes equation.
AB - This paper proposes a computer-assisted solution existence verification method for the stationary Navier–Stokes equation over general 3D domains. The proposed method verifies that the exact solution as the fixed point of the Newton iteration exists around the approximate solution through rigorous computation and error estimation. The explicit values of quantities required by applying the fixed-point theorem are obtained by utilizing newly developed quantitative error estimation for finite element solutions to boundary value problems and eigenvalue problems of the Stokes equation.
KW - Computer-assisted proof
KW - Finite element method
KW - Navier–Stokes equation
KW - Quantitative error estimation
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U2 - 10.1016/j.cnsns.2021.106223
DO - 10.1016/j.cnsns.2021.106223
M3 - Article
AN - SCOPUS:85123239004
SN - 1007-5704
VL - 108
JO - Communications in Nonlinear Science and Numerical Simulation
JF - Communications in Nonlinear Science and Numerical Simulation
M1 - 106223
ER -