A Novel Hierarchial Error Estimate for Elliptic Obstacle Problems

We present and analyze a novel hierarchical a posteriori error estimate for elliptic obstacle problems. The main result is that the energy norm of the finite element approximate error is, up to some extra oscillation term, equivalent to an appropriate hierarchical estimator. The proof is based upon some new observations on efficiency and some technical tools deriving from a previous work (Zou et al. in Numer. Math. 117:653-677, 2011). Moreover, we present an equivalence between the energy norm and the energy functional of the finite element approximate error. Several numerical experiments validate our theoretical findings.