I am looking for reference on how to implement nonlinear boundary conditions. Specifically, I am interested in implementing a radiation boundary condition for heat transfer with the FEM:
$-k \frac {\partial T} {\partial n} =F (T^{4} - T_{\infty}^{4})$
with $T$ temparature, $F$ is some factor, $k$ the thermal conductivity.
An ideal reference has the theory and a simple (1D/2D) example and possibly some code to try/verify. I have looked at Finite Element Analysis for Heat Transfer (Hou-Cheng Huang) but for the price the review was not favorable. Maybe some knows of some lecture nodes, a deal ii or fenics implementation I could look at?