ANALYSIS OF A BONE REMODELING MODEL

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.