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Zh. Vychisl. Mat. Mat. Fiz., 2014, Volume 54, Number 9, Pages 1515–1536 (Mi zvmmf10090)  

This article is cited in 4 scientific papers (total in 4 papers)

Domain decomposition method and numerical analysis of a fluid dynamics problem

A. V. Rukavishnikov

Institute of Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences, ul. Dzerzhinskogo 54, Khabarovsk, 680000, Russia

Abstract: A two-dimensional problem obtained by time discretization and linearization of a viscous flow governed by the incompressible Navier–Stokes equations is considered. The original domain is divided into subdomains such that their interface is a smooth (nonclosed, self-avoiding) curve with the ends belonging to the boundary of the domain. A nonconforming finite element method is constructed for the problem, and the convergence rate of the discrete solution of the problem to the exact one is estimated in the $L_2(\Omega_h)$ norm.

Key words: domain decomposition method, nonconforming finite element method, mortar elements, incompressible Navier–Stokes equations, estimate of the convergence rate of the discrete solution to the exact one.

DOI: https://doi.org/10.7868/S0044466914070102

Full text: PDF file (659 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2014, 54:9, 1459–1480

Bibliographic databases:

Document Type: Article
UDC: 519.634
Received: 25.05.2012
Revised: 16.01.2014

Citation: A. V. Rukavishnikov, “Domain decomposition method and numerical analysis of a fluid dynamics problem”, Zh. Vychisl. Mat. Mat. Fiz., 54:9 (2014), 1515–1536; Comput. Math. Math. Phys., 54:9 (2014), 1459–1480

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. E. M. Rudoy, “Numerical solution of an equilibrium problem for an elastic body with a delaminated thin rigid inclusion”, J. Appl. Industr. Math., 10:2 (2016), 264–276  mathnet  crossref  crossref  mathscinet  elib
    2. V. A. Rukavishnikov, A. V. Rukavishnikov, “Numerical analysis of a hydrodynamics problem with small viscosity”, International Conference on Analysis and Applied Mathematics 2015 (ICNAAM 2015) (Rhodes, Greece, 22–28 September 2015), AIP Conf. Proc., 1738, eds. T. Simos, C. Tsitouras, Amer. Inst. Phys., 2016, 030035  crossref  isi  scopus
    3. E. M. Rudoy, N. A. Kazarinov, V. Yu. Slesarenko, “Numerical simulation of the equilibrium of an elastic two-layer structure with a crack”, Num. Anal. Appl., 10:1 (2017), 63–73  mathnet  crossref  crossref  mathscinet  isi  elib
    4. N. A. Kazarinov, E. M. Rudoy, V. Yu. Slesarenko, V. V. Shcherbakov, “Mathematical and numerical simulation of equilibrium of an elastic body reinforced by a thin elastic inclusion”, Comput. Math. Math. Phys., 58:5 (2018), 761–774  mathnet  crossref  crossref  isi  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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