More on Convergence of Chorin’s Projection Method for Incompressible Navier–Stokes Equations

Masataka Maeda, Kohei Soga

Research output: Contribution to journalArticlepeer-review


Kuroki–Soga (Numer. Math. 146:401–433, 2020) proved that Chorin’s fully discrete finite difference projection method, originally introduced by Chorin (Math. Comput. 23:341–353, 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 to further exhibit mathematical aspects of the method. We show time-global solvability and convergence of the scheme; L2-error estimates for the scheme in the class of smooth exact solutions; application of the method to the problem with a time-periodic external force to investigate time-periodic (Leray–Hopf weak) solutions, long-time behaviors, error estimates, etc.

Original languageEnglish
Article number41
JournalJournal of Mathematical Fluid Mechanics
Issue number2
Publication statusPublished - 2022 May


  • Error estimate
  • Finite difference method
  • Fully discrete projection method
  • Incompressible Navier–Stokes equations
  • Leray–Hopf weak solution
  • Time-periodic solution

ASJC Scopus subject areas

  • Mathematical Physics
  • Condensed Matter Physics
  • Computational Mathematics
  • Applied Mathematics


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