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Sib. Zh. Vychisl. Mat., 2017, Volume 20, Number 4, Pages 425–437 (Mi sjvm661)  

This article is cited in 1 scientific paper (total in 1 paper)

A boundary value problem for one overdetermined stationary system emerging in the two-velocity hydrodynamics

M. V. Urevabc, Kh. Kh. Imomnazarova, Jian-Gang Tangd

a Institute of Computational Mathematics and Mathematical Geophysics SB RAS, 6 Lavrentiev av., Novosibirsk, 630090, Russia
b Novosibirsk State University, 2 Pirogova str., Novosibirsk, 630090, Russia
c Siberian Institute of Management — branch of the Russian Academy of National Economy and Public Service (RANE&PS), 6 Nizhegorodskya str., Novosibirsk, 630102, Russia
d YiLi Normal University, 448, Jiefang Road, Yinning Xinjiang, P.R. of China

Abstract: In this paper we investigate the two-velocity stationary hydrodynamics system with a single pressure and inhomogeneous divergent and boundary conditions for the two velocities. This system is overdetermined. By replacing the unknown functions, the problem is reduced to a homogeneous one. The solution of the resulting system is reduced to the consecutive solutions of the two boundary value problems: the Stokes problem for a single velocity and pressure, and overdetermined system for the other velocity. We present the generalized statements of these problems and their discrete approximation using the finite element method. To solve the overdetermined problem we apply a version of the regularization methods.

Key words: overdetermined two-velocity stationary hydrodynamics system, Lagrange multiplier, finite element method.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-11-00485П


DOI: https://doi.org/10.15372/SJNM20170406

Full text: PDF file (559 kB)
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English version:
Numerical Analysis and Applications, 2017, 10:4, 347–357

Bibliographic databases:

UDC: 519.632
Received: 10.01.2017
Revised: 18.05.2017

Citation: M. V. Urev, Kh. Kh. Imomnazarov, Jian-Gang Tang, “A boundary value problem for one overdetermined stationary system emerging in the two-velocity hydrodynamics”, Sib. Zh. Vychisl. Mat., 20:4 (2017), 425–437; Num. Anal. Appl., 10:4 (2017), 347–357

Citation in format AMSBIB
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\paper A boundary value problem for one overdetermined stationary system emerging in the two-velocity hydrodynamics
\jour Sib. Zh. Vychisl. Mat.
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\vol 20
\issue 4
\pages 425--437
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\crossref{https://doi.org/10.15372/SJNM20170406}
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\jour Num. Anal. Appl.
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\issue 4
\pages 347--357
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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. M. V. Urev, Sh. Kh. Imomnazarov, “Klassicheskoe reshenie odnoi pereopredelennoi statsionarnoi sistemy, voznikayuschei v dvukhskorostnoi gidrodinamike”, Sib. elektron. matem. izv., 15 (2018), 1621–1629  mathnet  crossref
  • Sibirskii Zhurnal Vychislitel'noi Matematiki
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