Analysis of new stabilized hp discontinuous Galerkin methods for elasticity problem

TL;DR

This paper introduces three innovative hp discontinuous Galerkin methods for elasticity problems, demonstrating their optimal convergence and validating results through numerical examples.

Contribution

The paper presents three new hp discontinuous Galerkin methods for elasticity, with proven optimal convergence rates and comparative analysis.

Findings

Optimal order of convergence in energy and L2 norms

Validation of theoretical results through numerical experiments

Comparison of three different numerical methods

Abstract

In the paper, we propose three new hp discontinuous Galerkin methods for the elasticity problem and make a comparison of the three numerical methods. And we prove the optimal order of convergence in energy norm and $L^2$-norm by the superpenalization technique. Finally, we give a numerical example to verify our theoretical results.