A Posteriori Error Estimators for Nonconforming Approximation

In this paper, an alternative approach for constructing an a posteriori error estimator for non-conforming approximation of scalar elliptic equation is introduced. The approach is based on the usage of post-processing conforming finite element approximation of the non-conforming solution . Then, the compatible a posteriori error estimator is defined by the local norms of difference between the nonconforming approximation and conforming postprocessing approximation on the element plus an additional residual term. We prove in general dimension the efficiency and the reliability of these estimators, without Helmholtz decomposition of the error, nor regularity assumption on the solution or the domain, nor saturation assumption. Finally explicit constants are given, which prove that these estimators are robust in suitable norms