Second order pressure estimates for the Crank-Nicolson discretization of the incompressible Navier-Stokes Equations
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, confirm...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
January 16, 2020
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| In: |
SIAM journal on numerical analysis
Year: 2020, Volume: 58, Issue: 1, Pages: 375-409 |
| ISSN: | 1095-7170 |
| DOI: | 10.1137/18M1234813 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1137/18M1234813
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| Author Notes: | Florian Sonner and Thomas Richter |
| Summary: | 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. |
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| Item Description: | Gesehen am 05.08.2020 |
| Physical Description: | Online Resource |
| ISSN: | 1095-7170 |
| DOI: | 10.1137/18M1234813 |