Unified Analysis of Discontinuous Galerkin Methods for Frictional Contact Problem with normal compliance

TL;DR

This paper develops and analyzes residual-based a posteriori error estimators for discontinuous Galerkin methods applied to frictional contact problems with normal compliance, providing both a priori and a posteriori error estimates.

Contribution

It introduces a reliable a posteriori error estimator and derives a priori error estimates for DG methods solving frictional contact problems modeled as quasi-variational inequalities.

Findings

Error estimator effectively guides adaptive mesh refinement.

Numerical results confirm the convergence and efficiency of the proposed methods.

The approach handles minimal regularity assumptions on the solution.

Abstract

In this article, a reliable and efficient a posteriori error estimator of residual type is derived for a class of discontinuous Galerkin methods for the frictional contact problem with reduced normal compliance which is modeled as a quasi-variational inequality. We further derive a priori error estimates in the energy norm under the minimal regularity assumption on the exact solution. The convergence behavior of error over uniform mesh and the performance of error estimator are illustrated by the numerical results.