Efficient and reliable hierarchical error estimates for the discretization error of elliptic obstacle problems

We present and analyze novel hierarchical a posteriori error estimates for self-adjoint elliptic obstacle problems. Our approach differs from straightforward, but nonreliable estimators by an additional extra term accounting for the deviation of the discrete free boundary in the localization step. We prove efficiency and reliability on a saturation assumption and a regularity condition on the underlying grid. Heuristic arguments suggest that the extra term is of higher order and preserves full locality. Numerical computations confirm our theoretical findings.