Uniform INF-SUP conditions for the spectral discretization of the Stokes problem

In standard spectral discretizations of the Stokes problem, error estimates on the pressure are slightly less accurate than the best approximation estimates, since the constant of the Babuska-Brezzi inf-sup condition is not bounded independently of the discretization parameter. In this paper, we propose two possible discrete spaces for the pressure: for each of them, we prove a uniform inf-sup condition, which leads in particular to an optimal error estimate on the pressure.