Spectral Element Discretization of the Circular Driven Cavity. Part III: The Stokes Equations in Primitive Variables

This paper deals with the spectral element discretization of the Stokes equations in a disk with discontinuous boundary data. The numerical treatment does not involve any regularization of these data. Based on a variational formulation in the primitive variables of velocity and pressure, we describe a discretization of the Stokes problem and derive error estimates in Sobolev spaces with appropriate weights. We propose an algorithm to solve the discrete system and present numerical experiments which confirm the efficiency of the method.