The spectral element discretization of the Stokes problem with mixed boundary conditions

The Stokes problem was reformulated using a variational approach with three independent unknowns vorticity, velocity, and pressure to manage boundary conditions involving the normal velocity component and tangential vorticity components. This work extends this formulation to accommodate mixed boundary conditions in three dimensional domains. A spectral element discretization is then applied to solve this problem, and a detailed numerical analysis is used to derive error estimates for three unknowns.