I need to solve let's say the heat equation over a domain made of two
different bodies. The heat flux must be discontinuous at the interface
between the two bodies.

So is the heat flux a variable in your formulation?

But thinking about it, what I imagine you want to say is not that the heat
flux is discontinuous, but that the gradient of the temperature is
discontinuous, right?

You're completely right. Sorry for not saying what I wanted to say, and thanks for guessing what I wanted to say from what I said!

Martin.
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