Convergence of the Finite Volume Method for a Conductive-Radiative Heat Transfer Problem

Abstract

We show that the finite volume method rigorously converges to the solution of a conductive-radiative heat transfer problem with nonlocal and nonlinear boundary conditions. To get this result, we start by proving existence of solutions for a finite volume discretization of the original problem. Then, by obtaining uniform boundedness of discrete solutions and their discrete gradients with respect to mesh size, we finally get L ₂ type convergence of discrete solutions.

Keywords:

• conductive-radiative heat transfer
• finite volume method
• nonlocal and nonlinear boundary conditions
• convergence

AMS Subject Classification:

• 35J65