Analysis of a model for the propagation of the ossification front

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• 作者：J.R. Ferná ; ndez ; ^{jose.fernandez@uvigo.es} ; M. Masid ^{maria.masid@gmail.com}
• 关键词：Ossification front ; Osteogenic cells ; Finite elements ; A priori estimates ; Numerical simulations
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：July 2017
• 年：2017
• 卷：318
• 期：Complete
• 页码：624-633
• 全文大小：672 K
• 卷排序：318

文摘

In this paper, we study a model for the propagation of the ossification front. This is written as a parabolic nonlinear partial differential equation in terms of the density of the osteogenic cells. Its variational formulation leads to a parabolic nonlinear variational equation for which an existence and uniqueness result is proved. Then, we introduce a fully discrete approximation by using the finite element method for the spatial approximation and a Euler scheme to discretize the time derivatives. A priori error estimates are obtained from which, under adequate additional regularity conditions, the linear convergence is derived. Finally, some numerical simulations are shown to demonstrate the accuracy and the influence of the approximation.