Approximation of Nonlinear Problems Associated with Radiating Bodies in Space

Abstract

Summary:In this paper we present a weak formulation of a two-dimensional stationary heat conduction problem with the radiation boundary condition. The problem can be described by an operator which is monotone on the convex set of admissible functions. The relation between classical and weak solutions as well as the convergence of the finite element method to the weak solution in the norm of the Sobolev space $H^1 (\Omega)$ are examined