I (with the help of Philippe Moireau and Patrick Le Tallec) just introduced a new formulation of the equilibrium gap principle in the context of finite element motion tracking, cf. https://doi.org/10.5802/crmeca.228! The code is available online (https://gitlab.inria.fr/mgenet/dolfin_warp), and there are even freely available Jupyter notebooks to reproduce the figures of the paper (https://mgenet.gitlabpages.inria.fr/N-DEG-paper-demos/index.html), so do not hesitate to give it a try!!
