On Error Estimates of Projection Methods for Navier–Stokes Equations: First-Order Schemes

In this paper projection methods (or fractional step methods) are studied in the semi-discretized form for the Navier–Stokes equations in a two- or three-dimensional bounded domain. Error estimates for the velocity and the pressure of the classical projection scheme are established via the energy method. A modified projection scheme which leads to improved error estimates is also proposed.