The spectral implementation of the nonstationary Stokes problem with nonstandard boundary conditions

Abstract

Abstract This paper deals with the implementation of the spectral discretization of the vorticity–velocity–pressure formulation of the nonstationary Stokes problem. We use the implicit Euler scheme for the discretization in time. We propose a global method for the resolution of the linear system resulting from the discrete problem. This method is implemented, and some numerical results are presented which confirm the good convergence for the three unknowns.

Keywords

• Stokes problem
• Vorticity–velocity–pressure formulation
• Spectral method
• Implicit Euler method