More on convergence of Chorin's projection method for incompressible Navier-Stokes equations

TL;DR

This paper extends previous work on Chorin's projection method, proving its global solvability and convergence for incompressible Navier-Stokes equations, with error estimates and applications to time-periodic solutions.

Contribution

It demonstrates time-global solvability and convergence of Chorin's scheme, providing $L^2$-error estimates and analyzing long-time behavior for time-periodic external forces.

Findings

Proved time-global solvability of the scheme.

Established $L^2$-error estimates for smooth solutions.

Analyzed long-time behavior and time-periodic solutions.

Abstract

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.