Existence of approximate solutions and error bounds for viscoelastic fluid flow: Characteristics method Original Research Article

In this paper we study a finite element approximation of a steady viscoelastic fluid flow obeying an Oldroyd B type constitutive law. The approximate stress, velocity, and pressure are, respectively, P1 discontinuous. P2 continuous, P1 continuous. We use the method of characteristics for the convection of the extra stress tensor. We suppose that the continuous problem admits a sufficiently smooth and sufficiently small solution. We show by a fixed point method that the approximate problem has a solution and an error bound is given.