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Hierarchical error estimates for the energy functional in obstacle problems. (English) Zbl 1218.65067

Authors’ abstract: 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 error in the energy minimum is, up to oscillation terms, equivalent to an appropriate hierarchical estimator. The proof does not invoke any saturation assumption. We even show that small oscillation implies a related saturation assumption. In addition, we prove efficiency and reliability of an a posteriori estimate of the discretization error and thereby cast some light on the theoretical understanding of previous hierarchical estimators. Finally, we illustrate our theoretical results by numerical computations.

MSC:

65K15 Numerical methods for variational inequalities and related problems
49J40 Variational inequalities
49M25 Discrete approximations in optimal control
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