Error analysis of an effective numerical scheme for a temporal multiscale plaque growth problem

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 $\mathrm{\Delta }T$, micro time step $\mathrm{\Delta }t$ and scale parameter $\epsilon$. A numerical example is presented to verify the theoretical results and demonstrate the excellent performance of the proposed multiscale algorithm.