Abstract

We provide optimal order pressure error estimates for the Crank--Nicolson semidiscretization of the incompressible Navier--Stokes equations. Second order estimates for the velocity error are long known; we prove that the pressure error is of the same order if considered at interval midpoints, confirming previous numerical evidence. For simplicity we first give a proof under high regularity assumptions that include nonlocal compatibility conditions for the initial data, then use smoothing techniques for a proof under reduced assumptions based on standard local conditions only.

Keywords

  1. incompressible Navier--Stokes
  2. Crank--Nicolson
  3. error estimates

MSC codes

  1. 76D05
  2. 65M15

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Information & Authors

Information

Published In

cover image SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Pages: 375 - 409
ISSN (online): 1095-7170

History

Submitted: 21 December 2018
Accepted: 12 November 2019
Published online: 16 January 2020

Keywords

  1. incompressible Navier--Stokes
  2. Crank--Nicolson
  3. error estimates

MSC codes

  1. 76D05
  2. 65M15

Authors

Affiliations

Funding Information

Federal Ministry of Education and Research of Germany : 05M16NMA
Deutsche Forschungsgemeinschaft https://doi.org/10.13039/501100001659 : 314838170
Deutsche Forschungsgemeinschaft https://doi.org/10.13039/501100001659 : GRK 2339

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