A locking free hp DPG method for linear elasticity with symmetric stresses

TL;DR

This paper introduces two innovative locking-free DPG methods for linear elasticity that achieve optimal accuracy for stress and displacement approximations, addressing issues of locking and interface discontinuities.

Contribution

The paper develops two new DPG methods for linear elasticity that are locking-free and provide optimal accuracy for both stress and displacement.

Findings

Locking-free convergence properties established

Optimal accuracy in both mesh size h and polynomial degree p

Analysis of interrelationships between the two methods

Abstract

We present two new methods for linear elasticity with simultaneously yield stress and displacement approximations of optimal accuracy in both the mesh size h and polynomial degree p. This is achieved within the recently developed discontinuous Petrov-Galerkin (DPG) framework. In this framework, both the stress and the displacement approximations are discontinuous across element interfaces. We study locking-free convergence properties and the interrelationships between the two DPG methods.