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 is 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.
Keith, B., Fuentes, F., & Demkowicz, L. (2016). The DPG methodology applied to different variational formulations of linear elasticity. Computer Methods in Applied Mechanics and Engineering, 309, 579–609. https://doi.org/10.1016/j.cma.2016.05.034