Approximation of bone remodeling models

Abstract

We present convergence results and error estimates concerning the numerical approximation of a class of bone remodeling models, that are elastic adaptive rod models. These are characterized by an elliptic variational equation, representing the equilibrium of the rod under the action of applied loads, coupled with an ordinary differential equation with respect to time, describing the physiological process of bone remodeling. We first consider the semi-discrete approximation, where only the space variables are discretized using the standard Galerkin method, and then, applying the forward Euler method for the time discretization, we focus on the fully discrete approximation.