A priori and a posteriori error bounds for a nonconforming linear finite element approximation of a non-newtonian flow

We consider a nonconforming linear finite element approximation of a non-Newtonian flow, where the viscosity obeys a Carreau type law for a pseudo-plastic. We prove optimal a priori error bounds for both the velocity and pressure. In addition we present a posteriori error estimators, which are based on the local valuation of the residuals. These yield global upper and local lower bounds for the error Finally, we perform some numerical experiments, which conflrm our a priori error bounds.