The method of Glowinski and Pironneaufor the unsteady stokes problem

The unsteady Stokes problem, i.e., the Stokes problem with a constant multiple of the velocity included in the velocity-pressure equation, is often central to methods used to solve the nonstationary Navier-Stokes equations and the equations governing viscoelastic flows. The Glowinski-Pironneau finite-element method for the Stokes problem decomposes the problem into a series of Poissonʹs equations, providing a potentially efficient approach for large problems in two or three dimensions. The goal of this paper is to present a complete development and analysis of the Glowinski-Pironneau method for the unsteady Stokes problem, along with numerical results which confirm the analytical estimates.