Pointwise a Posteriori Error Analysis for an Adaptive Penalty Finite Element Method for the Obstacle Problem

Abstract Finite element approximations based on a penalty formulation of the elliptic obstacle problem are analyzed in the maximum norm. A posteriori error estimates, which involve a residual of the approximation and a spatially variable penalty parameter, are derived in the cases of both smooth and rough obstacles. An adaptive algorithm is suggested and implemented in one dimension.

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