A convergence result for the approximation of the Navier-Stokes equations by an incremental projection method

An incremental projection method is proposed to approximate the Navier-Stokes equations. The error or? the velocity in the semi-discrete norm I-2(L-2(Omega)(d)) is shown to be O(delta t(2) + h(l+1)), where l greater than or equal to 1 is the polynomial degree of the velocity approximation. It is also shown that the splitting error of the projection schemes that are based on the incremental pressure correction is O(delta t(2)); this result holds even if the approximation of the time derivative of the velocity is O(delta t).