Preserving monotony of combined edge finite volume-finite element scheme for a bone healing model on general mesh

详细信息    查看全文

• 作者：Marianne Bessemoulin-Chatard^a ; ^{Marianne.Bessemoulin@univ-nantes.fr" class="auth_mail" title="E-mail the corresponding author} ; Mazen Saad^b ; ^{Mazen.Saad@ec-nantes.fr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Finite volume scheme ; Nonconforming finite element scheme ; Anisotropy ; Convergence analysis ; Bone healing model
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：1 January 2017
• 年：2017
• 卷：309
• 期：Complete
• 页码：287-311
• 全文大小：1224 K

文摘

In this article, we propose and analyze a combined finite volume–finite element scheme for a bone healing model. This choice of discretization allows to take into account anisotropic diffusions without imposing any restrictions on the mesh. Moreover, following the work of Cancès et al. (2013), we define a nonlinear correction of the diffusive terms to obtain a monotone scheme. We provide, under a numerical assumption, a complete convergence analysis of this corrected scheme, and present some numerical experiments which show its good behavior.