A finite element method for the axisymmetric three-field Stokes system with a discontinuous pressure

A quadrilateral based velocity-pressure-extrastress tensor mixed finite element method for solving the three-field Stokes system in the axisymmetric case is studied. The method derived from Fortin's Q2 − P1 velocity-pressure element is to be used in connection with the standard Galerkin formulation. This makes it particularly suitable for the numerical simulation of viscoelastic flow. It is proven to be second-order convergent in the natural weighted Sobolev norms, for the system under consideration. The crucial result that the method is uniformly stable is proven for the case of rectangular meshes. © 1999 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 15: 739–763, 1999