Pointwise A posteriori error control of quadratic Discontinuous Galerkin Methods for the unilateral contact problem

An a posteriori error bound for the pointwise error of the quadraticdiscontinuous Galerkin method for the unilateral contact problem on polygonaldomain is presented. The pointwise a posteriori error analysis is based on thedirect use of a priori estimates of the Green's matrix for the divergence typeoperators and the suitable construction of the discrete contact force density$\b{\sigma}_h$ and barrier functions for the continuous solution. Severalnumerical experiments (in two dimension) are presented to illustrate thereliability and efficiency properties of the proposed aposteriori errorestimator.