Error Analysis for Chorin's Original Fully Discrete Projection Method and Regularizations in Space and Time

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Abstract
Over twenty-five years ago, Chorin proposed a computationally efficient method for computing viscous incompressible flow which has influenced the development of efficient modern methods and inspired much analytical work. Using asymptotic error analysis techniques, it is now possible to describe precisely the kind of errors that are generated in the discrete solutions from this method and the order at which they occur. While the expected convergence rate is seen for velocity, the pressure accuracy is degraded by two effects: a numerical boundary layer due to the projection step and a global error due to the alternating or parasitic modes present in the discretization of the incompressibility condition. The error analysis of the projection step follows the work of E and Liu and the analysis of the alternating modes is due to the author. The two are combined to show the asymptotic character of the errors in the scheme. Regularization methods in space and time for recovering full accuracy for the computed pressure are discussed.