There are several variations of the Poisson problem with coupling.
One of them is within FESTIM itself (GitHub - RemDelaporteMathurin/FESTIM: My personal fork of FESTIM) and might be hard to parse.
We have several other versions floating around on discourse, including:
Discontinuity at interface using mixed domains - #2 by dokken
and the subsequent typo fix by @RemDelaporteMathurin
as well as:
Poisson submesh DG coupling · GitHub
(which is also cross posted multiple times on discourse: Search results for 'https://gist.github.com/jorgensd/8a5c32f491195e838f5863ca88b27bce' - FEniCS Project)