TY - GEN A1 - Zou, Qingsong A1 - Veeser, Andreas A1 - Kornhuber, Ralf A1 - Gräser, Carsten T1 - Hierarchical error estimates for the energy functional in obstacle problems N2 - We present a hierarchical a~posteriori error analysis for the minimum value of the energy functional in symmetric obstacle problems. The main result is that the energy of the exact solution is, up to data oscillation, equivalent to an appropriate hierarchical estimator. The proof of the main result does not invoke any saturation assumption. Moreover, we prove an a posteriori error estimate indicating that the estimator from \cite{RHWHoppe_RKornhuber_1994a} is asymptotically reliable and we give sufficient conditions for the validity of a saturation assumption. Finally, we corroborate and complement our theoretical results with numerical experiments. Y1 - 2009 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/578 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-5784 ER -