Nonconforming finite element approximation of the Giesekus model for polymer flows

We present a numerical approximation of the Giesekus equation which is considered as a realistic model for polymer flows. We use nonconforming finite elements on quadrilateral grids which necessitate the addition of two stabilization terms. An appropriate upwind scheme is employed for the convective term. The underlying discrete Stokes problem is then analysed. Finally, numerical tests are presented in order to validate the code, illustrating its good behavior for large Weissenberg numbers. Comparisons with Polyflow® and with the literature are also carried out.