Second order pressure estimates for the Crank-Nicolson discretization of the incompressible Navier-Stokes Equations

• Verfasst von: Sonner, Florian [VerfasserIn]
• Verfasst von: Richter, Thomas [VerfasserIn]
• Titel: Second order pressure estimates for the Crank-Nicolson discretization of the incompressible Navier-Stokes Equations
• Verf.angabe: Florian Sonner and Thomas Richter
• E-Jahr: 2020
• Jahr: January 16, 2020
• Umfang: 35 S.
• Fussnoten: Gesehen am 05.08.2020
• Titel Quelle: Enthalten in: Society for Industrial and Applied MathematicsSIAM journal on numerical analysis
• Ort Quelle: Philadelphia, Pa. : SIAM, 1966
• Jahr Quelle: 2020
• Band/Heft Quelle: 58(2020), 1, Seite 375-409
• ISSN Quelle: 1095-7170
• DOI: doi:10.1137/18M1234813
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: Crank-Nicolson
• Sach-SW: error analysis
• Sach-SW: error estimates
• Sach-SW: finite-element approximation
• Sach-SW: incompressible Navier-Stokes
• Sach-SW: stabilization
• Sach-SW: time
• K10plus-PPN: 1726254860

Abstract

We provide optimal order pressure error estimates for the Crank-Nicolson semidis-cretization 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.