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

Abstract

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, P 1 discontinuous. P 2 continuous, P 1 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.