I’ve just revised my codes, and I believe that manually setting the input/output electric current is enough to fully determine the electrostatic potential (voltage), up to a constant, of course. You can find such a MWE code at Lost with boundary conditions in ME spaces Daniel. Let me know what you think.
I do get consistent results (Ohm’s law safisfied), when I integrate the current density over the input and output surfaces I do get the correct current I have set. And I do get the full electrostatics potential field figured out everywhere, including on the boundaries, and it is far from being constant in my case (mixed element, coupling with temperature).