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

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          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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          Journal
          04 January 2024
          Article
          2401.02176
          29a20ac5-0c6f-4e07-b47c-6a9ec7e0df42

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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          math.NA cs.NA

          Numerical & Computational mathematics
          Numerical & Computational mathematics

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