Spectral discretization of the Navier-Stokes problem with mixed boundary conditions

摘要

We consider a variational formulation of the three dimensional Navier-Stokes equations provided with mixed boundary conditions. We write this formulation with three independent unknowns: the vorticity, the velocity and the pressure. Next, we propose a discretization by spectral methods. A detailed numerical analysis leads to a priori error estimates for the three unknowns.