  In this paper, we develop a new residual-based pointwise a posteriori error
estimator of the quadratic finite element method for the Signorini problem. The
supremum norm a posteriori error estimates enable us to locate the
singularities locally to control the pointwise errors. In the analysis the
discrete counterpart of contact force density is constructed suitably to
exhibit the desired sign property. We employ a priori estimates for the
standard Green's matrix for the divergence type operator and introduce the
upper and lower barriers functions by appropriately modifying the discrete
solution. Finally, we present numerical experiments that illustrate the
excellent performance of the proposed error estimator.
