On the consequence of discretization errors in the numerical calculation of viscoelastic flow

Having recalled some theorems pertaining to strong solutions of the viscoelastic flow problem, the authors establish a parallel between these theorems and observations made in the numerical calculation of such flows by means of a mixed method. Numerical errors in the evaluation of the extra-stress tensor have dramatic consequences upon the other field variables for the flow of a Maxwell fluid, and the damage is limited with an Oldroyd-B fluid.