A Posteriori Error Estimators for the Raviart–Thomas Element

Abstract

When error estimators for the Raviart–Thomas element are developed, two difficulties prevent the success of the straightforward application of frequently used arguments. The $H({\operatorname{div}},\Omega )$-norm is an anisotropic norm; i.e., it refers to differential operators of different orders. Moreover, the traces of $H({\operatorname{div}},\Omega )$-functions are only in $H^{ - {1 / 2}} $. Therefore, one does not obtain optimal a posteriors error estimates when using natural norms. This drawback is overcome by using mesh-dependent norms.