An optimal three-field finite element approximation of the Stokes system with continuous extra stresses

Abstract

The aim of this paper is to present a mixed finite element method for solving the twodimensional Stokes system, written in terms of the variables velocity, pressure and extra stress tensor. A convenient functional framework is introduced, allowing simpler choices of the type of approximation for the third variable. This is assumed here to be continuous, in order to ensure its applicability to viscoelastic flow problems. In the particular second order Galerkin method that is studied, the dimension of the corresponding finite element subspace is reduced to a minimum, at least as far as local stability analyses are concerned.