Splitting a Concave Domain to Convex Subdomains

Abstract

We examine a steady-state heat radiation problem and its finite element approximation in $R^d$, $d=2, 3$. A nonlinear Stefan-Boltzmann boundary condition is considered. Another nonlinearity is due to the fact that the temperature is always greater or equal than $0 [K]$. We prove two convergence theorems for piecewise linear finite element solutions.