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Pointwise A posteriori error control of quadratic Discontinuous Galerkin Methods for the unilateral contact problem (2401.02176v1)

Published 4 Jan 2024 in math.NA and cs.NA

Abstract: 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 $\b{\sigma}_h$ 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.

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