Cardone, Giuseppe; Panasenko, Grigory P.; Sirakov, Yvan Asymptotic analysis and numerical modeling of mass transport in tubular structures. (English) Zbl 1200.35021 Math. Models Methods Appl. Sci. 20, No. 3, 397-421 (2010). 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. Cited in 8 Documents 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 Keywords:partial asymptotic decomposition of domain; Stokes equation; convection-diffusion equation; thin structure PDFBibTeX XMLCite \textit{G. Cardone} et al., Math. Models Methods Appl. Sci. 20, No. 3, 397--421 (2010; Zbl 1200.35021) Full Text: DOI arXiv References: [1] Panasenko G. P., Multi-Scale Modelling for Structures and Composites (2005) · Zbl 1078.74002 [2] DOI: 10.1080/00036810008840890 · Zbl 1034.35097 · doi:10.1080/00036810008840890 [3] DOI: 10.1515/9783110848915 · doi:10.1515/9783110848915 [4] DOI: 10.1007/978-1-4612-5364-8 · doi:10.1007/978-1-4612-5364-8 [5] DOI: 10.1007/978-1-4757-4317-3 · doi:10.1007/978-1-4757-4317-3 [6] DOI: 10.1142/S021820259800007X · Zbl 0940.35026 · doi:10.1142/S021820259800007X [7] DOI: 10.1142/S0218202599000609 · Zbl 1035.76010 · doi:10.1142/S0218202599000609 [8] DOI: 10.1080/00036810410001712826 · Zbl 1064.35019 · doi:10.1080/00036810410001712826 [9] Panasenko G. P., C. R. Mech. Acad. Sci. Paris, Ser. IIb 327 pp 1185– [10] DOI: 10.1016/j.na.2005.06.034 · Zbl 1103.35029 · doi:10.1016/j.na.2005.06.034 [11] Ciarlet P. G., The Finite Element Method for Elliptic Problems (1978) · Zbl 0383.65058 [12] Panasenko G. P., Int. J. Multisci. Comput. Engrg. 5 pp 473– [13] Grisvard P., Elliptic Problems in Nonsmooth Domains (1985) · Zbl 0695.35060 [14] Nicaise S., Ann. Sci. Norm. Sup. Pisa 20 pp 163– [15] Solonnikov V. A., College France Sem. 4 pp 240– This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.