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

초록

In this work we propose a new and simple way of reconstructing H(div, Omega)-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, Omega)-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. (C) 2012 IMACS. Published by Elsevier B.V. All rights reserved.

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