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Long‐time stability and asymptotic analysis of the IFE method for the multilayer porous wall model
Author(s) -
Zhang Huili,
Wang Kun
Publication year - 2018
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22206
Subject(s) - discretization , mathematics , stability (learning theory) , euler's formula , temporal discretization , scheme (mathematics) , backward euler method , exponential stability , finite element method , porous medium , euler method , porosity , elliptic curve , mathematical analysis , materials science , computer science , physics , thermodynamics , nonlinear system , quantum mechanics , machine learning , composite material
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‐statef ¯ ( x ) in bothL 1 ( 0 , t ; L 2 ( Ω ) ) andL ∞ ( 0 , t ; L 2 ( Ω ) ) norms as t → + ∞ . Finally, some numerical experiments are given to verify the theoretical predictions.