Numerical analysis of a FEM for a transient viscoelastic flow Original Research Article

We present the numerical analysis of a coupled method for the numerical simulation of transient viscoelastic flows obeying a differential constitutive equation with a Newtonian viscosity. The scheme used is based on Euler implicit method in time and maintain at each time step a coupling between the velocity u and the viscoelastic part of the stress σ. Approximation in space is made by finite element method (FE). The approximate stress, velocity and pressure are, respectively, P1—discontinuous, P2—continuous and P1—continuous. Upwinding needed for convection of σ is made by a discontinuous Galerkin FE method.