A stable finite element method for the axisymmetric three-field Stokes system

Abstract A rectangular based velocity-pressure-extra-stress tensor mixed finite element method for solving the three-field Stokes system in the axisymmetric case is studied. The method is to be used in connection with the standard Galerkin formulation, which 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.