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Abstract
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.
Mathematics Subject Classification: Primary: 74B20, 65N15; Secondary: 74S05.
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