An $hp$-version error analysis of the discontinuous Galerkin method for linear elasticity

TL;DR

This paper develops an $hp$-version error analysis for the discontinuous Galerkin method applied to linear elasticity, providing theoretical error estimates and supporting numerical experiments.

Contribution

It introduces new $hp$-version error estimates for the DG method in mixed formulation for linear elasticity, extending previous techniques.

Findings

Error estimates in energy and $L^2$ norms are established.

Numerical experiments confirm the theoretical error bounds.

Abstract

An $hp$-version error analysis is developed for the general DG method in mixed formulation for solving the linear elastic problem. First of all, we give the $hp$-version error estimates of two $L^2$ projection operators. Then incorporated with the techniques in [11], we obtain the $hp$-version error estimates in energy norm and $L^2$ norm. Some numerical experiments are provided for demonstrating the theoretical results.