Discrete Reliability for Crouzeix-Raviart FEMs

The discrete reliability states that the difference of the discrete solutions on two arbitrary levels u` and u`+m with respect to triangulations T` and T`+m is bounded by the contributions of the residual-based error estimator on the refined simplices T` \ T`+m only. After some natural split of the error, the additional difficulty for the nonconforming FEMs is to bound min v`+m∈CR(T`+m) ‖∇NC(u` − v`+m)‖2L2(Ω)