Approximate Transmission Conditions for a Poisson Problem at Mid-Diffusion
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...
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| Format: | Article |
| Language: | English |
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Vilnius Gediminas Technical University
2015-02-01
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| Series: | Mathematical Modelling and Analysis |
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| Online Access: | https://journals.vgtu.lt/index.php/MMA/article/view/984 |
| _version_ | 1818765444338679808 |
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| author | Khaled El-Ghaouti Boutarene |
| author_facet | Khaled El-Ghaouti Boutarene |
| author_sort | Khaled El-Ghaouti Boutarene |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-18T08:18:11Z |
| format | Article |
| id | doaj.art-ad0d0a3f57cf41e18a37f2fe83f11173 |
| institution | Directory Open Access Journal |
| issn | 1392-6292 1648-3510 |
| language | English |
| last_indexed | 2024-12-18T08:18:11Z |
| publishDate | 2015-02-01 |
| publisher | Vilnius Gediminas Technical University |
| record_format | Article |
| series | Mathematical Modelling and Analysis |
| spelling | doaj.art-ad0d0a3f57cf41e18a37f2fe83f111732022-12-21T21:14:47ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102015-02-0120110.3846/13926292.2015.1000988Approximate Transmission Conditions for a Poisson Problem at Mid-DiffusionKhaled El-Ghaouti Boutarene0USTHB, Faculty of Mathematics, AMNEDP Laboratory, PO Box 32, El Alia 16111, Bab Ezzouar, Algiers, AlgeriaThis 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.https://journals.vgtu.lt/index.php/MMA/article/view/984asymptotic analysisasymptotic expansionapproximate transmission conditionsthin layerPoisson equation |
| spellingShingle | Khaled El-Ghaouti Boutarene Approximate Transmission Conditions for a Poisson Problem at Mid-Diffusion Mathematical Modelling and Analysis asymptotic analysis asymptotic expansion approximate transmission conditions thin layer Poisson equation |
| title | Approximate Transmission Conditions for a Poisson Problem at Mid-Diffusion |
| title_full | Approximate Transmission Conditions for a Poisson Problem at Mid-Diffusion |
| title_fullStr | Approximate Transmission Conditions for a Poisson Problem at Mid-Diffusion |
| title_full_unstemmed | Approximate Transmission Conditions for a Poisson Problem at Mid-Diffusion |
| title_short | Approximate Transmission Conditions for a Poisson Problem at Mid-Diffusion |
| title_sort | approximate transmission conditions for a poisson problem at mid diffusion |
| topic | asymptotic analysis asymptotic expansion approximate transmission conditions thin layer Poisson equation |
| url | https://journals.vgtu.lt/index.php/MMA/article/view/984 |
| work_keys_str_mv | AT khaledelghaoutiboutarene approximatetransmissionconditionsforapoissonproblematmiddiffusion |