Approximation of Nonlinear Problems Associated with Radiating Bodies in Space

Abstract

This paper presents an efficient and reliable method to approximate the solution of nonlinear boundary value problems describing the temperature distribution in a radiating body in space. A variational formulation is constructed for an arbitrary radiation law in $T^p $, $p \geqq 1$ an integer. The minimizing element of an appropriate functional is shown to coincide with the solution of the initial problem. The solution is approximated by the finite element method. Nonlinear programming techniques are discussed and a new fast and stable iterative method is presented.