Suppose I have to solve the 2-D heat equation in a rectangular domain using the finite difference method, for the boundary conditions say:$T_1$ is the temperature of the right side of the rectangle,$T_2$ is the temperature of the top side,$T_3$ is the temperature of the left side,and $T_4$ is the temperature at the bottom.           T2    _______________   |               |T3 |               |T1   |               |   |_______________|          T4at the vertices points of the rectangle, how to set the boundary conditions? do I need to take the average value of the two temperatures?Regards
How to set the temperature at the vertices points for a rectangular domain?
finite difference
I believe you cannot apply two boundary conditions at the same point. You need to choose between T2 and T3 for the top-left point for instance. The average might be acceptable but I'm not sure of the physical meaning though.Anyway, with a fine discretization, it should not be a problem since the consequence of this choice will be insignificant on the solution.