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.
Boutarene, K. E.-G. (2015). Approximate Transmission Conditions for a Poisson Problem at Mid-Diffusion. Mathematical Modelling and Analysis, 20(1), 53-75. https://doi.org/10.3846/13926292.2015.1000988
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