On a FEM method for a linearized version of the Oldroyd’s problem Original Research Article

We present a study of a finite element method (FEM) for the approximation of a linearized version of the Oldroyd’s problem. The method, is based on a work in [ZAMM 65 (1985) 449] concerning the continuous problem, on a splitting of the momentum equation and on a modification of the streamline upwind Petrov Galerkin method in [Comput. Meth. Appl. Mech. Engrg. 45 (1984) 285]. It is also formally connected to the modified elastic viscous split stress method in [J. Non-Newtonian Fluid Mech. 60 (1995) 27]. This method allows us to improve some numerical results expected for more standard methods, in particular, we obtain convergence results in the case of a null Newtonian fraction of the viscosity.