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In this paper, we develop a new residual-based pointwise a posteriori errorestimator of the quadratic finite element method for the Signorini problem. Thesupremum norm a posteriori error estimates enable us to locate thesingularities locally to control the pointwise errors. In the analysis thediscrete counterpart of contact force density is constructed suitably toexhibit the desired sign property. We employ a priori estimates for thestandard Green's matrix for the divergence type operator and introduce theupper and lower barriers functions by appropriately modifying the discretesolution. Finally, we present numerical experiments that illustrate theexcellent performance of the proposed error estimator.

Supremum norm A Posteriori Error control of Quadratic Finite Element Method for the Signorini problem