CONVERGENCE OF NUMERICAL SCHEMES FOR A CONSERVATION EQUATION WITH CONVECTION AND DEGENERATE DIFFUSION

作     者：R.Eymard C.Guichard Xavier Lhebrard R.Eymard;C.Guichard;Xavier Lhébrard

作者机构：Universite Gustave EiffelLaboratoire d'nalyse et de Mathematiques Appliquees(UMR 8050)UGEUPECCNRSF-77454Mame-la-ValleeFrance Sorbonne UniversiteUniversite Paris-Diderot SPCCNRSInriaLaboratoire Jacques-Louis Lionsequipe ANGEF-75005 Paris Ecole Normale Superieure de RennesFrance 

出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)

年 卷 期：2021年第39卷第3期

页      面：428-452页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：supported by the French Agence Nationale de la Recherche(CHARMS project ANR-16-CE06-0009) 

主　　题：Linear convection Degenerate diffusion Gradient discretisation method θ-scheme 

摘      要：The approximation of problems with linear convection and degenerate nonlinear difFusion,which arise in the framework of the transport of energy in porous media with thermodynamic transitions,is done usingθ-scheme based on the centred gradient discretisation *** convergence of the numerical scheme is proved,although the test functions which can be chosen are restricted by the weak regularity hypotheses on the convection field,owing to the application of a discrete Gronwall lemma and a general result for the time translate in the gradient discretisation *** numerical examples,using both the Control Volume Finite Element method and the Vertex Approximate Gradient scheme,show the role ofθfor stabilising the scheme.