An improved inf—sup condition for the spectral discretization of the Stokes problem in a cylinder Original Research Article

We propose a spectral discretization of the Stokes problem in a cylinder, that relies on the approximation by Fourier series with respect to the angular variable and high degree polynomials with respect to the radial and axial variables. The aim of this paper is to prove some optimal Babuška—Brezzi type conditions between appropriate discrete spaces of velocity and pressure, in order to derive the best possible error estimates on the pressure.