Long‐time stability and asymptotic analysis of the IFE method for the multilayer porous wall model

E-ISSN： 1098-2426|34|2|419-441

ISSN： 0749-159x

Source： NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Vol.34, Iss.2, 2018-03, pp. : 419-441

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Abstract

In this article, we study the long‐time stability and asymptotic behavior of the immersed finite element (IFE) method for the multilayer porous wall model for the drug‐eluting stents. First, with the IFE method for the spatial descretization, and the implicit Euler scheme for the temporal discretization, respectively, we deduce the global stability of fully discrete solution. Then, we investigate the asymptotic behavior of the discrete scheme which reveals that the multilayer porous wall model converges to the corresponding elliptic equation if $f (x, t)$ approaches to a steady‐state $\bar{f} (x)$ in both $L^{1} (0, t; L^{2} (Ω))$ and $L^{\infty} (0, t; L^{2} (Ω))$ norms as $t \to + \infty$ . Finally, some numerical experiments are given to verify the theoretical predictions.