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Second order pressure estimates for the Crank-Nicolson discretization of the incompressible Navier-Stokes equations. (English) Zbl 1448.76066

Summary: 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.

MSC:

76D05 Navier-Stokes equations for incompressible viscous fluids
76M20 Finite difference methods applied to problems in fluid mechanics
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs

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References:

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