ON THE APPROXIMATION OF THE UNSTEADY NAVIER-STOKES EQUATIONS BY FINITE-ELEMENT PROJECTION METHODS

This paper provides an analysis of a fractional-step projection method to compute incompressible viscous flows by means of finite element ap proximations. The analysis is based on the idea that the appropriate f unctional setting for projection methods must accommodate two differen t spaces for representing the velocity fields calculated respectively in the viscous and the incompressible half steps of the method. Such a theoretical distinction leads to a finite element projection method w ith a Poisson equation for the incremental pressure unknown and to a v ery practical implementation of the method with only the intermediate velocity appearing in the numerical algorithm. Error estimates in fini te time are given. An extension of the method to a problem with unconv entional boundary conditions is also considered to illustrate the flex ibility of the proposed method.