Convergence of the finite volume method for a conductive-radiative heat transfer problem - Birgelis, Karlis; Raitums, Uldis (Mathematical Modelling and Analysis, 2013)
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 2type convergence of discrete solutions.