Method of asymptotic partial decomposition of domain for multistructures

Abstract

Method of asymptotic partial decomposition of a domain (MAPDD) proposed and justified earlier for thin domains (rod structures, tube structures) is generalized and justified for the multistructures, i.e. domains consisting of a set of thin cylinders connecting some massive 3D domains. In the present paper, the Dirichlet boundary value problem for the steady-state Stokes equations is considered. This problem is reduced to the Stokes equations in the massive domains coupled with the Poiseuille-type flows within the thin cylinders at some distance from the bases (the MAPDD approximation problem). The high-order estimates for the difference of the exact solution to the initial problem and the solution to the MAPDD approximation problem is proved.

Keywords:

• Stokes equations
• multistructures
• asymptotic partial decomposition
• estimates
• hybrid dimension models

AMS Subject Classifications:

• 35Q35
• 76D07
• 65N55

Notes

No potential conflict of interest was reported by the author.

Additional information

Funding

The work was financially supported by the [grant number 14-11-00306] of Russian Scientific Foundation operated by the Moscow Power Engineering Institute (Technical University) and by LABEX MILYON (ANR-10-LABX-0070) of University of Lyon, within the program “Investissements d’Avenir” (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR).