The algorithmic resolution of spectral-element discretization for the time-dependent Stokes problem

Abstract

Abstract We consider two algorithms for the resolution of the time-dependent Stokes problem with nonstandard boundary conditions by the domain-decomposition spectral-element method. The first algorithm (Elimination method) is based on the Uzawa method by decoupling the linear system, while the second algorithm (Global inversion) is based on the overall resolution of the system by the GMRES method. A detailed implementation is proposed and some numerical tests are carried out in two and three dimensions and where the domain is multiply connected.

Keywords

• Time-dependent Stokes problem
• Spectral-element method
• Implicit Euler scheme
• Uzawa algorithm
• GMRES method