I am trying to implement a boundary condition where the rate of change of my function at the boundary depends on the value of the function at this boundary in a nonlinear way. How can I implement his?
As far as I understand, I can use the expression
∂nu = g : -int1d(Th)( g*w)
for Neumann boundary conditions. But what if g itself depends on the value of the unknown function u?
Are you looking for the Robin boundary condition (g(u) linear with u)? Then you may start here: Laplace eigenproblem with Robin boundary condition
If the Robin BC is nonlinear, you may have to implement a nonlinear solution of your problem.
Dear Vincent, thanks for your reply. Actually, I want to model thermal radiation from the surface of a plate. Therefore, the local gradient at the boundary should be du/dx=u^4, since radiation scales with the fourth power of the surface temperature. Would this fall in the category of a Robin boundary condition? Am I on a good road if use the int1d term?