QUASI-NORM ERROR-BOUNDS FOR THE FINITE-ELEMENT APPROXIMATION OF A NON-NEWTONIAN FLOW

We consider the finite element approximation of a non-Newtonian flow, where the viscosity obeys a general law including the Carreau or power law. For sufficiently regular solutions we prove energy type error bo unds for the velocity and pressure. These bounds improve on existing r esults in the literature. A key step in the analysis is to prove abstr act error bounds initially in a quasi-norm, which naturally arises in degenerate problems of this type.