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 quadratic discontinuous Galerkin method for the unilateral contact problem on polygonal domain is presented. The pointwise a posteriori error analysis is based on the direct use of a priori estimates of the Green’s matrix for the divergence type operators and the suitable construction of the discrete contact force density $\text{b}{\sigma }_h$ and barrier functions for the continuous solution. Several numerical experiments (in two dimension) are presented to illustrate the reliability and efficiency properties of the proposed aposteriori error estimator.