  In this work, we propose a simple numerical scheme based on a fast
front-tracking approach for solving a fluid-structure interaction (FSI) problem
of plaque growth in blood vessels. A rigorous error analysis is carried out for
the temporal semi-discrete scheme to show that it is first-order accurate for
all macro time step $\Delta T$, micro time step $\Delta t$ and scale parameter
$\epsilon$. A numerical example is presented to verify the theoretical results
and demonstrate the excellent performance of the proposed multiscale algorithm.
