A new mixed finite element method for the Stokes problem

We propose a new mixed formulation of the Stokes problem where the extra stress tensor is considered. Based on such a formulation, a mixed finite element is constructed and analyzed. This new finite element has properties analogous to the finite volume methods, namely, the local conservation of the momentum and the mass. Optimal error estimates are derived. For the numerical implementation of this finite element, a hybrid form is presented. This work is a first step towards the treatment of viscoelastic fluid flows by mixed finite element methods.