Correctors and error estimates for reaction-diffusion processes through thin heterogeneous layers in case of homogenized equations with interface diffusion

• Verfasst von: Gahn, Markus [VerfasserIn]
• Verfasst von: Jäger, Willi [VerfasserIn]
• Verfasst von: Neuss-Radu, Maria [VerfasserIn]
• Titel: Correctors and error estimates for reaction-diffusion processes through thin heterogeneous layers in case of homogenized equations with interface diffusion
• Verf.angabe: Markus Gahn, Willi Jaeger, Maria Neuss-Radu
• E-Jahr: 2020
• Jahr: 1 August 2020
• Umfang: 29 S.
• Teil: volume:383
• Teil: year:2020
• Teil: extent:29
• Fussnoten: Gesehen am 12.11.2020
• Titel Quelle: Enthalten in: Journal of computational and applied mathematics
• Ort Quelle: Amsterdam [u.a.] : North-Holland, 1975
• Jahr Quelle: 2020
• Band/Heft Quelle: 383(2020) Artikel-Nummer 113126, 29 Seiten
• ISSN Quelle: 1879-1778
• DOI: doi:10.1016/j.cam.2020.113126
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: Asymptotic analysis
• Sach-SW: Boundary layers
• Sach-SW: Correctors
• Sach-SW: effective transmission conditions
• Sach-SW: Error estimates
• Sach-SW: limit behavior
• Sach-SW: Reaction-diffusion equations
• Sach-SW: sieve
• Sach-SW: Thin heterogeneous layer
• Sach-SW: viscous-fluid flow
• K10plus-PPN: 1738560708

Abstract

In this paper, we construct approximations of the microscopic solution of a nonlinear reaction-diffusion equation in a domain consisting of two bulk-domains, which are separated by a thin layer with a periodic heterogeneous structure. The size of the heterogeneities and thickness of the layer are of order epsilon, where the parameter epsilon is small compared to the length scale of the whole domain. In the limit epsilon -> 0, when the thin layer reduces to an interface Sigma separating two bulk domains, a macroscopic model with effective interface conditions across Sigma is obtained. Our approximations are obtained by adding corrector terms to the macroscopic solution, which take into account the oscillations in the thin layer and the coupling conditions between the layer and the bulk domains. To validate these approximations, we prove error estimates with respect to epsilon. Our approximations are constructed in two steps leading to error estimates of order epsilon(1/2) and epsilon in the H-1-norm. (C) 2020 Elsevier B.V. All rights reserved.