Existence Theory for the Solution of a Stationary Nonlinear Conductive‐Radiative Heat‐Transfer Problem in Three Space Dimensions

2004 ◽  
Vol 33 (5-7) ◽  
pp. 563-576 ◽  
Author(s):  
M. Thompson ◽  
C. Segatto ◽  
M. T. de Vilhena
Keyword(s):  
Heat Transfer ◽  
Radiative Heat Transfer ◽  
Radiative Heat ◽  
Transfer Problem ◽  
Heat Transfer Problem ◽  
Existence Theory ◽  
Three Space

scholarly journals CONVERGENCE OF THE FINITE VOLUME METHOD FOR A CONDUCTIVE-RADIATIVE HEAT TRANSFER PROBLEM

2013 ◽  
Vol 18 (2) ◽  
pp. 274-288 ◽  
Author(s):  
Karlis Birgelis ◽  
Uldis Raitums
Keyword(s):  
Heat Transfer ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Radiative Heat Transfer ◽  
Radiative Heat ◽  
Transfer Problem ◽  
Uniform Boundedness ◽  
Mesh Size ◽  
Heat Transfer Problem ◽  
Volume Method

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.

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