Computer-assisted proof for the stationary solution existence of the Navier–Stokes equation over 3D domains

Xuefeng Liu*, Mitsuhiro T. Nakao, Shin'ichi Oishi

*この研究の対応する著者

研究成果: Article査読

抄録

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.

本文言語English
論文番号106223
ジャーナルCommunications in Nonlinear Science and Numerical Simulation
108
DOI
出版ステータスPublished - 2022 5月

ASJC Scopus subject areas

  • 数値解析
  • モデリングとシミュレーション
  • 応用数学

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