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

VL - 108

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

SN - 1007-5704

M1 - 106223

ER -