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Asymptotic analysis and numerical modeling of mass transport in tubular structures. (English) Zbl 1200.35021

Summary: The flow in a thin tubular structure is considered. The velocity of the flow stands for a coefficient in the convection-diffusion equation set in the thin structure. An asymptotic expansion of solution is constructed. This expansion is used further for justification of an asymptotic domain decomposition strategy essentially reducing the memory and the time of the code. A numerical solution obtained by this strategy is compared to the numerical solution obtained by a direct FEM computation.

MSC:

35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
35Q30 Navier-Stokes equations
76M45 Asymptotic methods, singular perturbations applied to problems in fluid mechanics
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
35B40 Asymptotic behavior of solutions to PDEs
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References:

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