Enhanced algorithms for implementing the spectral discretization of the vorticity‐velocity‐pressure formulation of Stokes problem

In this paper, we deal with the numerical resolution of spectral discretization of the vorticity‐velocity‐pressure formulation of Stokes problem in a square or a cube provided with nonstandard boundary conditions, which involve the normal component of the velocity and the tangential components of the vorticity. Therefore, we propose two algorithms: the Uzawa algorithm and the global resolution. We implemented the two algorithms and compared their results. With global resolution, we obtained a very good accuracy with a small number of iteration.