NUMERICAL ANALYSIS OF A FEM FOR A TRANSIENT VISCOELASTIC FLOW

We present the numerical analysis of a coupled method for the numerical simulation of transient viscoelastic flow obeying a differential constitutive equation with a Newtonian viscosity. The scheme used is based on Euler implicit method in time and maintains at each time step a couple of the velocity u and the viscoelastic part of the stress σ. Approximation in space is made by finite element method. The approximate stress, velocity and pressure are, respectively, P1-continuous, p2-continuous, and p1continuous. Upwinding needed for convection of σ is made by a "Streamline Upwind Petrov Galerkin" method (SUPG).