论文标题
有关不可压缩的Navier-Stokes方程的Chorin投影方法的融合的更多信息
More on convergence of Chorin's projection method for incompressible Navier-Stokes equations
论文作者
论文摘要
kuroki和soga [numer。数学。 2020年]证明了Chorin的完全离散投影方法，最初由A. J. Chorin [Math]引入。 comp。 1969]，在任意固定时间间隔内无条件地解决和收敛，以与具有任意外力的有界域上不可压缩的Navier-Stokes方程的Leray-Hopf弱解。本文是Churoki-Soga的作品的延续。我们显示了我们方案的时间全球溶解度和收敛性； $ l^2 $ -ERROR估算平滑精确解决方案中的计划；将该方案应用于问题，以时间周期性的外力来研究时间周期性（leray-hopf弱）解决方案，长期行为，错误估计等。
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.
