Kuroki and Soga [Numer. Math. 2020] proved that a version of Chorin's fully discrete projection method, originally introduced by A. J. Chorin [Math. Comp. 1969], is unconditionally solvable and convergent within an arbitrary fixed time interval to a Leray-Hopf weak solution of the incompressible Navier-Stokes equations on a bounded domain with an arbitrary external force. This paper is a continuation of Kuroki-Soga's work. We show time-global solvability and convergence of our scheme; $L^2$-error estimates for the scheme in the class of smooth exact solutions; application of the scheme to the problem with a time-periodic external force to investigate time-periodic (Leray-Hopf weak) solutions, long-time behaviors, error estimates, etc.

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更多关于不可压缩 Navier-Stokes 方程的 Chorin 投影方法的收敛性

黑木和苏我 [Numer. 数学。2020] 证明了最初由 AJ Chorin [Math. 比较 1969] 是无条件可解的，并且在任意固定时间间隔内收敛到具有任意外力的有界域上不可压缩 Navier-Stokes 方程的 Leray-Hopf 弱解。本文是 Kuroki-Soga 工作的延续。我们展示了我们方案的时间全局可解性和收敛性；$L^2$-光滑精确解类中方案的误差估计；将该方案应用于具有时间周期外力的问题，以研究时间周期（Leray-Hopf 弱）解、长时间行为、误差估计等。