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Sibirskii Zhurnal Vychislitel'noi Matematiki
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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2019, Volume 22, Number 4, Pages 437–451
DOI: https://doi.org/10.15372/SJNM20190404 (Mi sjvm724) 		 
This article is cited in 3 scientific papers (total in 3 papers)

A solution of the degenerate Neumann problem by the finite element method

M. I. Ivanova, I. A. Kremerab, M. V. Urevba

a Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch, Russian Academy of Sciences, pr. Akad. Lavrent’eva 6, Novosibirsk, 630090 Russia
b Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090 Russia
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DOI: https://doi.org/10.15372/SJNM20190404
Abstract: This paper deals with the solution of the degenerate Neumann problem for the diffusion equation by the finite element method. First, an extended generalized formulation of the Neumann problem in the Sobolev space H1(Ω) is derived and investigated. Then a discrete analogue of this problem is formulated using standard finite element approximations of the space H1(Ω). An iterative method for solving the corresponding SLAE is proposed. Some examples of solving the model problems are used to discuss the numerical peculiarities of the algorithm proposed.
Key words: degenerate Neumann problem, matching conditions, orthogonalization of the right-hand side, finite elements.
Received: 18.03.2019
Accepted: 25.07.2019
English version:
Numerical Analysis and Applications, 2019, Volume 12, Issue 4, Pages 359–371
DOI: https://doi.org/10.1134/S1995423919040049
Bibliographic databases:
Document Type: Article
UDC: 519.632
Language: Russian
Citation: M. I. Ivanov, I. A. Kremer, M. V. Urev, “A solution of the degenerate Neumann problem by the finite element method”, Sib. Zh. Vychisl. Mat., 22:4 (2019), 437–451; Num. Anal. Appl., 12:4 (2019), 359–371
Citation in format AMSBIB
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\by M.~I.~Ivanov, I.~A.~Kremer, M.~V.~Urev
\paper A solution of the degenerate Neumann problem by the finite element method
\jour Sib. Zh. Vychisl. Mat.
\yr 2019
\vol 22
\issue 4
\pages 437--451
\mathnet{http://mi.mathnet.ru/sjvm724}
\crossref{https://doi.org/10.15372/SJNM20190404}
\transl
\jour Num. Anal. Appl.
\yr 2019
\vol 12
\issue 4
\pages 359--371
\crossref{https://doi.org/10.1134/S1995423919040049}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000513714900004}
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  • https://www.mathnet.ru/eng/sjvm724
  • https://www.mathnet.ru/eng/sjvm/v22/i4/p437
    • This publication is cited in the following 3 articles:
    1. Bruno A. Roccia, Carmina Alturria Lanzardo, Fernando D. Mazzone, Cristian G. Gebhardt, “On the homogeneous torsion problem for heterogeneous and orthotropic cross-sections: Theoretical and numerical aspects”, Applied Numerical Mathematics, 201 (2024), 579  crossref
    2. Maksim I. Ivanov, Igor A. Kremer, Yuri M. Laevsky, “On non-uniqueness of pressures in problems of fluid filtration in fractured-porous media”, Journal of Computational and Applied Mathematics, 425 (2023), 115052  crossref
    3. M. I. Ivanov, I. A. Kremer, Yu. M. Laevsky, “Solving the Pure Neumann Problem by a Mixed Finite Element Method”, Numer. Analys. Appl., 15:4 (2022), 316  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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