Augmented spectral formulation for the Stokes problem with variable viscosity and mixed boundary conditions

This paper deals with the analysis of a new augmented formulation in terms of vorticity, velocity and pressure for the Stokes equations with variable viscosity and mixed boundary conditions. The well-posedness of the continuous problem holds under assumptions on the viscosity. When the domain is a parallelepiped, the spectral discretization is proposed using the Galerkin method with numerical integration. Then, we prove the well-posedness of the obtained discrete problem under the same type of conditions on the viscosity. A priori error estimates is then derived for the three unknowns. Finally, numerical experiments are presented that confirm the interest of the discretization.