Error estimates for MAC-like approximations to the linear Navier-Stokes equations

SummaryIn this paper a priori error estimates are derived for the discretization error which results when the linear Navier-Stokes equations are solved by a method which closely resembles the MAC-method of Harlow and Welch. General boundary conditions are permitted and the estimates are in terms of the discreteL2 norm. A solvability result is given which also applies to a generalization of the method to the nonlinear case. This generalization is used in the last section to produce a numerical solution to the problem of flow around an obstacle.

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