A-PRIORI AND A-POSTERIORI ERROR-BOUNDS FOR A NONCONFORMING LINEAR FINITE-ELEMENT APPROXIMATION OF A NON-NEWTONIAN FLOW

We consider a nonconforming linens finite element approximation of a n on-Newtonian flow, where the viscosity obeys a Carreau type law for a pseudo-plastic. We prove optimal a priori error bounds for both the ve locity and pressure. In addition we present a posteriori error estimat ors, which are based on the local evaluation of the residuals. These y ield global upper and local lower bounds for the error. Finally, we pe rform some numerical experiments, which confirm our a priori error bou nds. (C) Elsevier, Paris.