Using the Finite Volume Method, one can discretise a PDE in the following way:
But what I don't understand is why the minus sign (highlighted with yellow) appears in the equation below. It feels that it should be the plus sign, yet it must be the minus sign. I would appreciate if someone could please clarify.
I suspect that $u_j = g_j$ for $j\in n_i\cap m$. This term is moved to the rhs. The minus sign is the sign of $u_i$ in the red formula above.