ERROR ANALYSIS FOR CHORIN ORIGINAL FULLY DISCRETE PROJECTION METHOD AND REGULARIZATIONS IN SPACE AND TIME

Over twenty-five years ago, Chorin proposed a computationally efficien t method for computing viscous incompressible flow which has influence d the development of efficient modern methods and inspired much analyt ical work. Using asymptotic error analysis techniques, it is now possi ble 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 pressu re accuracy is degraded by two effects: a numerical boundary layer due to the projection step and a global error due to the alternating or p arasitic 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 a uthor. The two are combined to show the asymptotic character of the er rors in the scheme. Regularization methods in space and time for recov ering full accuracy for the computed pressure are discussed.