Approximate transmission conditions for a Poisson problem at\n mid-diffusion

2013/09/18 by Khaled El-Ghaouti Boutarene, Boutarene, Khaled El-Ghaouti
Computer Science · Engineering · #35B40 #35C20 #35J25 #41A60 #78M35 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1309.4597

openalex publication_date 2013/09/18 · openalex created_date 2022/08/21 · openalex updated_date 2026/07/28

Abstract

This work consists in the asymptotic analysis of the solution of Poisson\nequation in a bounded domain of \ℝ^P (P=2,3) with a thin layer.\nWe use a method based on hierarchical variational equations to derive\nasymptotic expansion of the solution with respect to the thickness of the thin\nlayer. We determine the first three terms of the expansion and prove the error\nestimate made by truncating the expansion after a finite number of terms. Next,\nusing the first two terms of the asymptotic expansion, we show that we can\nmodel the effect of the thin layer by a problem with transmission conditions of\norder two.\n

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