  This paper is concerned with the PDE and numerical analysis of a modified
one-dimensional intravascular stent model originally proposed in [4]. It is
proved that the modified model has a unique weak solution using the Galerkin
method combined with a compactness argument. A semi-discrete finite element
method and a fully discrete scheme using the Euler time-stepping are formulated
for the PDE model. Optimal order error estimates in the energy norm are proved
for both schemes. Numerical results are presented along with comparisons
between different decoupling strategies and time-stepping schemes. Lastly,
extensions of the model and its PDE and numerical analysis results to the
two-dimensional case are also briefly discussed.
