A-POSTERIORI ERROR ESTIMATORS FOR NONCONFORMING APPROXIMATION OF SOMEQUASI-NEWTONIAN FLOWS

This paper deals with a posteriori error estimators for nonconforming approximations of quasi-Newtonian hows. We consider the Crouzeix-Ravia rt piecewise linear approximations of scalar elliptic problems and def ine an error estimator. When Omega is a simply connected domain, the e rror is dominated by the estimator. This estimator can be generalized to higher-order elements. We define a posteriori error estimators for the Fortin-Soulie piecewise quadratic approximations of quasi-Newtonia n flows and prove that the error is dominated by the estimator. This e stimator can be computed locally in terms of the approximate solution and is therefore suitable for adaptive refinement.