Numerical Approximation of a Nonlinear 3D Heat Radiation Problem

In this paper, we are concerned with the numerical approximation ofa steady-state heat radiation problem with a nonlinear Stefan-Boltzmann boundarycondition in$mathbb{R}^3$. We first derive an equivalent minimization problem and thenpresent a finite element analysis to the solution of such a minimization problem.Moreover, we apply the Newton iterative method for solving the nonlinear equationresulting from the minimization problem. A numerical example is given toillustrate theoretical results.