Space and time error estimates for a first order, pressure stabilized finite element method for the incompressible Navier-Stokes equations

In this paper we analyze a pressure stabilized, finite element method for t he unsteady, incompressible Navier-Stokes equations in primitive variables; for the time discretization we focus on a fully implicit, monolithic schem e. We provide some error estimates for the fully discrete solution which sh ow that the velocity is first order accurate in the time step and attains o ptimal order accuracy in the mesh size for the given spatial interpolation, both in the spaces L-2(Omega) and H-0(1)(Omega); the pressure solution is shown to be order 1/2 accurate in the time step and also optimal in the mes h size. These estimates are proved assuming only a weak compatibility condi tion on the approximating spaces of velocity and pressure, which is satisfi ed by equal order interpolations. (C) 2001 IMACS. Published by Elsevier Sci ence B.V. All rights reserved.