TY - JOUR

T1 - More on Convergence of Chorin’s Projection Method for Incompressible Navier–Stokes Equations

AU - Maeda, Masataka

AU - Soga, Kohei

N1 - Funding Information:
The authors thank one of the reviewers for pointing out the reference [] and []. The second author, Kohei Soga, is supported by JSPS Grant-in-aid for Young Scientists #18K13443.
Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

PY - 2022/5

Y1 - 2022/5

N2 - 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.

AB - 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.

KW - Error estimate

KW - Finite difference method

KW - Fully discrete projection method

KW - Incompressible Navier–Stokes equations

KW - Leray–Hopf weak solution

KW - Time-periodic solution

UR - http://www.scopus.com/inward/record.url?scp=85126802830&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85126802830&partnerID=8YFLogxK

U2 - 10.1007/s00021-021-00652-5

DO - 10.1007/s00021-021-00652-5

M3 - Article

AN - SCOPUS:85126802830

SN - 1422-6928

VL - 24

JO - Journal of Mathematical Fluid Mechanics

JF - Journal of Mathematical Fluid Mechanics

IS - 2

M1 - 41

ER -