Vorticity–velocity–pressure formulation for Navier–Stokes equations

Abstract

We analyze here the bidimensional boundary value problems, for both Stokes and Navier–Stokes equations, in the case where non standard boundary conditions are imposed. A well-posed vorticity–velocity–pressure formulation for the Stokes problem is introduced and its finite element discretization, which needs some stabilization, is then studied. We consider next the approximation of the Navier–Stokes equations, based on the previous approximation of the Stokes equations. For both problems, the convergence of the numerical approximation and optimal error estimates are obtained. Some numerical tests are also presented.