Remarks on the state of the art of a posteriori error control of elliptic PDEs in energy norms in practise (Q2891137)

Five classes of up to 9 a posteriori error estimators compete in three second-order model problems, namely the conforming and nonconforming first-order approximation of the Poisson problem plus some conforming obstacle problem. The authors' numerical results provide sufficient evidence that guaranteed error control in the energy norm. The five classes of error estimators consist of the standard residual-based error estimators, averaging error estimators, equilibration error estimators, least-square error estimators and the localisation error estimator of Carstensen and Funken.