ON THE VELOCITY-VORTICITY FORMULATION OF THE 2-DIMENSIONAL STOKES SYSTEM AND ITS FINITE-ELEMENT APPROXIMATION

This paper deals with the numerical study of the two-dimensional Stoke s equations in terms of the velocity and the vorticity. We take one of the possible sets of boundary conditions, for which the equivalence b etween the standard velocity-pressure Stokes system and such velocity- vorticity formulation holds. We consider the corresponding rigorous va riational framework and an uncoupled solution scheme. In this context, the authors proposed several families of Galerkin finite element appr oximations, for which they derived optimal or suboptimal convergence r esults. Here their numerical approach is illustrated by several numeri cal examples. As a byproduct, hints are given on the best way to inter polate the different fields involved in the analogous uncoupling schem e, for solving the incompressible Navier-Stokes equations.