Spectral discretization of the time‐dependent vorticity–velocity–pressure formulation of the Stokes problem

Abstract

In this paper, we study the time‐dependent vorticity–velocity–pressure formulation of Stokes problem in two‐ and three‐dimensional domains provided with nonstandard boundary conditions, related to the normal component of the velocity and the tangential components of the vorticity. This problem is discretized by implicit Euler's scheme in time and spectral method in space. We prove an optimal error estimate for the three unknowns.