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January  2009, 8(1): 255-274. doi: 10.3934/cpaa.2009.8.255

Analysis of a bone remodeling model

J. R. Fernández 1, , R. Martínez 1, and  J. M. Viaño 1,

1. 

Departamento de Matemática Aplicada, Universidade de Santiago de Compostela, Facultade de Matemáticas, Campus Sur s/n, 15782 Santiago de Compostela, Spain, Spain, Spain

Received  April 2008 Revised  August 2008 Published  October 2008

In this work we study, from the numerical point of view, a bone remodeling model. The variational formulation of this problem is written as an elliptic variational equation for the displacement field, coupled with a first-order ordinary differential equation, with respect to the time, to describe the physiological process of bone remodeling. Fully discrete approximations are introduced, based on the finite element method to approximate the spatial variable, and on an Euler scheme to discretize the time derivatives. Error estimates are obtained on the approximate solutions, from which the linear convergence of the algorithm is derived under suitable regularity conditions. Finally, some numerical results, involving examples in one, two and three dimensions, are presented to show the accuracy and the performance of the algorithm.
Keywords: fully discrete approximations, Bone remodeling, numerical simulations, error estimates.
Mathematics Subject Classification: Primary: 74B20, 65N15; Secondary: 74S05.
Citation: J. R. Fernández, R. Martínez, J. M. Viaño. Analysis of a bone remodeling model. Communications on Pure and Applied Analysis, 2009, 8 (1) : 255-274. doi: 10.3934/cpaa.2009.8.255
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