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- W2095408052 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. On présente des résultats de convergence et d'estimation d'erreur concernant l'approximation numérique d'une classe de modèles de remodelage des os, et qui correspondent à une classe de modèles de poutres en élasticité adaptative. Ces modèles sont caracterisés par une équation variationnelle elliptique, réprésentant l'équilibre d'une poutre sous l'action des forces appliquées, couplée avec une équation differentielle par raport au temps, décrivant le processus biologique de remodelage d'un os. On considère tout d'abord l'approximation semi-discrète, en discrétisant les variables spatiales et en utilisant une méthode de Galerkin standard, puis on applique la méthode d'Euler pour la discrétisation en temps, et finalement on analyse l'approximation discrète complète." @default.
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- W2095408052 date "2005-12-01" @default.
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- W2095408052 title "Approximation of bone remodeling models" @default.
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- W2095408052 doi "https://doi.org/10.1016/j.matpur.2005.07.006" @default.
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