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dc.contributor.authorGhattassi, Mohamed
dc.contributor.authorRoche, Jean Rodolphe
dc.contributor.authorSchmitt, Didier
dc.date.accessioned2018-12-31T13:10:48Z
dc.date.available2018-12-31T13:10:48Z
dc.date.issued2018-07-11
dc.identifier.citationGhattassi M, Roche JR, Schmitt D (2019) Analysis of a full discretization scheme for 2D radiative–conductive heat transfer systems. Journal of Computational and Applied Mathematics 346: 1–17. Available: http://dx.doi.org/10.1016/j.cam.2018.06.028.
dc.identifier.issn0377-0427
dc.identifier.doi10.1016/j.cam.2018.06.028
dc.identifier.urihttp://hdl.handle.net/10754/630422
dc.description.abstractThis 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.
dc.description.sponsorshipWe would like to thank the CAM corresponding editor and the anonymous referees for their suggestions which led to the improvement of the original manuscript.
dc.publisherElsevier BV
dc.relation.urlhttp://www.sciencedirect.com/science/article/pii/S0377042718303807
dc.subjectRadiative-conductive heat transfer
dc.subjectGalerkin method
dc.subjectCrank–Nicolson scheme
dc.subjectBanach fixed point theorem
dc.subjectError estimates
dc.titleAnalysis of a full discretization scheme for 2D radiative-conductive heat transfer systems
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.identifier.journalJournal of Computational and Applied Mathematics
dc.contributor.institutionUniversity of Lorraine, IECL UMR CNRS 7502, 54506 Vandoeuvre-lès-Nancy, France
kaust.personGhattassi, Mohamed
dc.date.published-online2018-07-11
dc.date.published-print2019-01


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