Implementation of the spectral element discretization of the nonstationary velocity–vorticity–pressure Stokes formulation

Abstract

Abstract This paper deals with the resolution of the time-dependent velocity–vorticity–pressure formulation of Stokes problem in a two- and three-dimensional domain. The discretization is based on the spectral element method with respect to the space variable and Euler’s implicit scheme with respect to the time variable. We implement the asymmetric linear system to solve the full spectral element discrete problem. Detailed numerical experiments lead to confirm the usefulness of the discretization.

Keywords

• Nonstationary Stokes problem
• Spectral element method
• Implicit Euler scheme
• GMRES algorithm