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

A steady-state convection-diffusion problem with a small diffusion of order O(epsilon) is considered in a thin three-dimensional graph-like junction consisting of thin cylinders connected through a domain (node) of diameter O(epsilon), where epsilon 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 H-1 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 epsilon.

Automated summary

This article considers a steady-state convection-diffusion problem with a small diffusion factor in a thin three-dimensional graph-like junction composed of thin cylinders connected through a domain. The asymptotic expansion for the solution is constructed and justified using multiscale analysis. Asymptotic estimates in the norm of Sobolev space H-1 and the uniform norm are proved for the difference between the solution and proposed approximations, with a predetermined accuracy based on the level of the small parameter.