The DPG methodology applied to different variational formulations of linear elasticity

TL;DR

This paper demonstrates the flexibility of the DPG methodology by applying it to various variational formulations of linear elasticity, including non-symmetric cases, and provides numerical evidence of its effectiveness in 3D problems.

Contribution

It explores the application of DPG to different variational formulations of linear elasticity, including non-symmetric and broken energy space formulations, with numerical validation.

Findings

All formulations are well-posed in broken energy spaces.

Numerical results confirm expected convergence rates.

DPG effectively solves 3D elasticity problems with smooth and singular solutions.

Abstract

The flexibility of the DPG methodology is exposed by solving the linear elasticity equations under different variational formulations, including some with non-symmetric functional settings (different infinite-dimensional trial and test spaces). The family of formulations presented are proved to be mutually ill or well-posed when using traditional energy spaces on the whole domain. Moreover, they are shown to remain well-posed when using broken energy spaces and interface variables. Four variational formulations are solved in 3D using the DPG methodology. Numerical evidence is given for both smooth and singular solutions and the expected convergence rates are observed.