| Abstract: | In this paper, we propose and numerically investigate a superconvergentcluster recovery (SCR) method for the Crouzeix-Raviart (CR) element. The proposedrecovery method reconstructs a $C^0$ linear gradient. A linear polynomial approximation is obtained by a least square fitting to the CR element approximation at certainsample points, and then taken derivatives to obtain the recovered gradient. The SCRrecovery operator is superconvergent on uniform mesh of four patterns. Numericalexamples show that SCR can produce a superconvergent gradient approximation forthe CR element, and provide an asymptotically exact error estimator in the adaptiveCR finite element method. |
