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Convergence of the finite volume method for a conductive-radiative heat transfer problem

    Karlis Birgelis Affiliation
    ; Uldis Raitums Affiliation

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 2type convergence of discrete solutions.

Keyword : conductive-radiative heat transfer, finite volume method, nonlocal and nonlinear boundary conditions, convergence

How to Cite
Birgelis, K., & Raitums, U. (2013). Convergence of the finite volume method for a conductive-radiative heat transfer problem. Mathematical Modelling and Analysis, 18(2), 274-288. https://doi.org/10.3846/13926292.2013.783885
Published in Issue
Apr 1, 2013
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