Approximate Transmission Conditions for a Poisson Problem at Mid-Diffusion

Mathematical Modelling and Analysis

Khaled El-Ghaouti Boutarene¹ 

[1] USTHB, Faculty of Mathematics, AMNEDP Laboratory, PO Box 32, El Alia 16111, Bab Ezzouar, Algiers, Algeria;

关键词: asymptotic analysis;    asymptotic expansion;    approximate transmission conditions;    thin layer;    Poisson equation;   

DOI  :  10.3846/13926292.2015.1000988

来源: DOAJ

【 摘 要 】

This work consists in the asymptotic analysis of the solution of Poisson equation in a bounded domain of RP(P = 2, 3) with a thin layer. We use a method based on hierarchical variational equations to derive an explicitly asymptotic expansion of the solution with respect to the thickness of the thin layer. We determine the first two terms of the expansion and prove the error estimate made by truncating the expansion after a finite number of terms. Next, using the first two terms of the asymptotic expansion, we show that we can model the effect of the thin layer by a problem with transmission conditions of order two.

【 授权许可】

Unknown