A posteriori error estimators for nonconforming approximation of some quasi-Newtonian flows

This paper deals with a posteriori error estimators for nonconforming approximations of quasi-Newtonian hows. We consider the Crouzeix-Raviart piecewise linear approximations of scalar elliptic problems and define an error estimator. When Omega is a simply connected domain, the error 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-Newtonian flows and prove that the error is dominated by the estimator. This estimator can be computed locally in terms of the approximate solution and is therefore suitable for adaptive refinement.