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We present and analyze novel hierarchical a posteriori error es- timates for self-adjoint elliptic obstacle problems. Our approach differs from straightforward, but non-reliable estimators (9) by an additional extra term ac- counting 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.

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