Spectral discretization of the time‐dependent Stokes problem with mixed boundary conditions

Abstract

In this paper, we consider the time-dependent Stokes problem in a three-dimensional domain with mixed boundary conditions. The discretization relies on spectral methods with respect to the space variables and Euler's implicit scheme with respect to the time variable, then by the second order BDF method. A detailed numerical analysis leads to a priori error estimates for each numerical scheme.