Asymptotic expansion for the solution of a convection-diffusion problem in a thin graph-like junction

Article type: Research Article

Authors: Mel’nyk, Taras A.^{; *} | Klevtsovskiy, Arsen V.

Affiliations: Department of Mathematical Physics, Taras Shevchenko National University of Kyiv, Volodymyrska st., 64/13, Kyiv 01601, Ukraine

Correspondence: [*] Corresponding author. E-mail: melnyk@imath.kiev.ua.

Abstract: A steady-state convection-diffusion problem with a small diffusion of order O(ε) is considered in a thin three-dimensional graph-like junction consisting of thin cylinders connected through a domain (node) of diameter O(ε), where ε is a small parameter. Using multiscale analysis, the asymptotic expansion for the solution is constructed and justified. The asymptotic estimates in the norm of Sobolev space H1 as well as in the uniform norm are proved for the difference between the solution and proposed approximations with a predetermined accuracy with respect to the degree of ε.

Keywords: Asymptotic expansion, convection-diffusion problem, asymptotic estimate, thin graph-like junction

DOI: 10.3233/ASY-221761

Journal: Asymptotic Analysis, vol. 130, no. 3-4, pp. 505-530, 2022