This paper deals with the convergence of numerical scheme for combined nonlinear radiation-conduction heat transfer system in a gray, absorbing and non-scattering two-dimensional medium. The radiative transfer equation is solved using a Discontinuous Galerkin method with upwind fluxes. The conductive equation is discretized using the finite element method. Moreover, the Crank–Nicolson scheme is applied for time discretization of the semi-discrete nonlinear coupled system. Existence and uniqueness of the solution for the continuous and full discrete system are presented. The convergence proof follows from the application of a discrete fixed-point theorem, involving only the temperature fields at each time step. The order of approximation error, stability, and order of convergence are investigated. Finally, the theoretical stability and convergence results are supported with numerical examples.
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledgements: We would like to thank the CAM corresponding editor and the anonymous referees for their suggestions which led to the improvement of the original manuscript.