A VELOCITY PRESSURE STREAMLINE DIFFUSION FINITE-ELEMENT METHOD FOR THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS

In this paper a streamline diffusion finite element method is introduced for the time-dependent incompressible Navier-Stokes equations in a bounded domain in R2 and R3 in the case of high Reynolds number flow. An error estimate is proved and numerical results are given. The method is based on a mixed velocity-pressure formulation using the same finite element discretization of space-time for the velocity and the pressure spaces, which consist of piecewise linear functions, together with certain least-squares modifications of the Galerkin variational formulation giving added stability without sacrificing accuracy. © 1990.