Long time error estimates of IFE methods for the unsteady multi-layer porous wall model

Abstract In this paper, we study the immersed finite element (IFE) method for the multi-layer porous wall model for the drug-eluting stents. Firstly, under some realistic assumptions on the initial data and the body force, we deduce the long time p r i o r i stability for the variational problem for all t ∈ R + . Then, based on these results, the uniform optimal error estimates for both the semi-discrete IFE method and the fully discrete Euler IFE method are proved. Finally, some numerical experiments are performed to verify the theoretical predictions.