NUMERICAL-ANALYSIS OF A FEM FOR A TRANSIENT VISCOELASTIC FLOW

We present the numerical analysis of a coupled method for the numerica l simulation of transient viscoelastic flows obeying a differential co nstitutive equation with a Newtonian viscosity. The scheme used is bas ed on Euler implicit method in time and maintain at each time step a c oupling between the velocity u and the viscoelastic part of the stress sigma. Approximation in space is made by finite element method (FE). The approximate stress, velocity and pressure are, respectively, P-1-d iscontinuous, P-2-continuous and P-1-continuous. Upwinding needed for convection of sigma is made by a discontinuous Galerkin FE method.