Analysis of a model for the propagation of the ossification front

In this paper, we study a model for the propagation of the ossification front. This is written as a parabolic nonlinear partial differential equation in terms of the density of the osteogenic cells. Its variational formulation leads to a parabolic nonlinear variational equation for which an existence and uniqueness result is proved. Then, we introduce a fully discrete approximation by using the finite element method for the spatial approximation and a Euler scheme to discretize the time derivatives. A priori error estimates are obtained from which, under adequate additional regularity conditions, the linear convergence is derived. Finally, some numerical simulations are shown to demonstrate the accuracy and the influence of the approximation.