An extra stress - vorticity formulation of Stokes problem for the Oldroyd viscoelastic model

We present a three fields formulation of the Stokes problem with the following unknowns: σ¯ extra stress tensor, ψ stream function and ω vorticity. This formulation is motivated by the Oldroyd model for viscoelastic flows. In fact, it appears that problems in (σ¯,ω) and ψ are uncoupled and moreover that the problem (σ¯,ω) reduces to the solution of two laplacians and one (u, p) Stokes problem.An another important feature is that the symmetry of the stresses is dualized. The purpose of this paper is to describe this new formulation, to show that it satisfies an inf-sup condition and that classical finite element spaces can be used for its approximation.