Hello Stein and anyone else reading/interested,
Just so you know, I have created a thread about my weak form (Deriving the weak form of my problem, is it correct?). I think I have understood a bit more what happens when I don’t specify any boundary condition on some boundaries, and to answer my own question, what happens isn’t that any flux vanishes there, but that \nabla T and \nabla V have no normal component there. But a flux, for example TS\vec J may have a normal component there.
I am 99% sure my weak form is correct, and that the results are making a lot of sense.
Now regarding
Indeed, I will try to figure this out myself. I wonder also, is there a smart way to retrieve any flux using the accurate way, not just the one that pops up from the weak form? If I had to choose right now, I’d be interested in \vec J_U, \vec J and TS\vec J as well. Should I try to figure out what kind of weak form yields those fluxes?