Flux reconstruction for the P2 nonconforming finite element method with application to a posteriori error estimation

In this work we propose a new and simple way of reconstructing H(div,Ω)-conforming flux approximations for the P2 nonconforming finite element method of second order elliptic problems which fulfill the local mass conservation and optimal a priori error estimates. This reconstruction is crucially used in deriving an a posteriori error estimator which gives a guaranteed upper bound on the actual error. We also apply the same technique to the Stokes problem in order to reconstruct a H(div,Ω)-conforming pseudo-tensor approximation which are then used for a posteriori error estimation. Some numerical results are presented to illustrate the performance of the error estimators thus obtained.