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Analysis and convergence of the MAC scheme. II: Navier-Stokes equations. (English) Zbl 0852.76066
Summary: The MAC discretization scheme for the incompressible Navier-Stokes equations is interpreted as a covolume approximation to the equations. Using some results from earlier papers (in particular, part I of the present work [the first author, SIAM J. Numer. Anal. 29, No. 6, 1579-1591 (1992; Zbl 0764.76051)]) dealing with covolume error estimates for div-curl equation systems, and under certain conditions on the data and the solutions of the Navier-Stokes equations, we obtain first-order error estimates for both the vorticity and the pressure.

MSC:
76M25 Other numerical methods (fluid mechanics) (MSC2010)
76D05 Navier-Stokes equations for incompressible viscous fluids
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
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