A Stabilized Finite Element Approximation Of Viscoelastic Fluid Flow

This paper is devoted to the numerical analysis of a stabilized finite element approximation for viscoelastic fluid flow obeying an Oldroyd B type constitutive law. The approximate stress, velocity and pressure are respectively Pkdiscontinuous, Pk+1 continuous and Pk continuous for an arbitrary integer k > 0.The method of Lesaint-Raviart for the convection of the extra stress tensor is used. When assuming the continuous problem admits a sufficiently smooth and sufficiently small solution, the approximate problem is proved to have a unique solution by employing a fixed point method, and an error estimate is derived.