V. A. Rukavishnikov, E. V. Kuznetsova, “A scheme of a finite element method for boundary value problems with non-coordinated degeneration of input data”, Sib. Zh. Vychisl. Mat., 12:3 (2009), 313–324; Num. Anal. Appl., 2:3 (2009), 250

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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2009, Volume 12, Number 3, Pages 313–324 (Mi sjvm25)

This article is cited in 13 scientific papers (total in 13 papers)

A scheme of a finite element method for boundary value problems with non-coordinated degeneration of input data

V. A. Rukavishnikov^a, E. V. Kuznetsova^b

^a Computer Centre Far-Eastern Branch of RAS
^b Far Eastern State Transport University

Full-text PDF (244 kB) Citations (13)

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Abstract: We construct a scheme of a finite element method for boundary value problems with non-coordinated degeneration of input data and singularity of solution. The rate of convergence of an approximate solution of the proposed finite element method to the exact

R_{ν}

$R_{\nu}$ -generalized solution in the weight set

W_{2, ν^{*} + β / 2 + 1}^{1} (Ω, δ)

$W^1_{2,\nu^*+\beta/2+1}(\Omega,\delta)$ is investigated, the estimation of finite element approximations is established.

Key words: non-coordinated degeneration of input data,

R_{ν}

$R_{\nu}$ -generalized solution, singularity of a solution, finite element method.

Received: 14.11.2007
Revised: 21.07.2008

English version:
Numerical Analysis and Applications, 2009, Volume 2, Issue 3, Pages 250–259
DOI: https://doi.org/10.1134/S1995423909030069

Bibliographic databases:

UDC: 519.632

Language: Russian

Citation: V. A. Rukavishnikov, E. V. Kuznetsova, “A scheme of a finite element method for boundary value problems with non-coordinated degeneration of input data”, Sib. Zh. Vychisl. Mat., 12:3 (2009), 313–324; Num. Anal. Appl., 2:3 (2009), 250–259

Citation in format AMSBIB

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\jour Sib. Zh. Vychisl. Mat.

\yr 2009

\vol 12

\issue 3

\pages 313--324

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\transl

\jour Num. Anal. Appl.

\yr 2009

\vol 2

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\crossref{https://doi.org/10.1134/S1995423909030069}

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Linking options:

https://www.mathnet.ru/eng/sjvm25

https://www.mathnet.ru/eng/sjvm/v12/i3/p313

This publication is cited in the following 13 articles:

Viktor A. Rukavishnikov, Elena I. Rukavishnikova, “Weighted finite element method and body of optimal parameters for elasticity problem with singularity”, Computers & Mathematics with Applications, 151 (2023), 408
V. A. Rukavishnikov, A. V. Rukavishnikov, “Metod chislennogo resheniya odnoi statsionarnoi zadachi gidrodinamiki v konvektivnoi forme v $L$ -obraznoi oblasti”, Kompyuternye issledovaniya i modelirovanie, 12:6 (2020), 1291–1306
Rukavishnikov V.A., Rukavishnikova I E., “Finite Element Methods With the Special Graded Mesh For Elliptic Equation With Degeneration on the Entire Boundary”, AIP Conference Proceedings, 2293, eds. Simos T., Tsitouras C., Amer Inst Physics, 2020, 100007
V. A. Rukavishnikov, A. O. Mosolapov, “Vesovoi vektornyi metod konechnykh elementov i ego prilozheniya”, Kompyuternye issledovaniya i modelirovanie, 11:1 (2019), 71–86
E. I. Rukavishnikova, “Skhodimost metoda konechnykh elementov dlya kraevoi zadachi s vyrozhdeniem na vsei granitse oblasti”, Vestn. YuUrGU. Ser. Vych. matem. inform., 8:3 (2019), 5–26
Rukavishnikov V.A., Rukavishnikova E.I., “Existence and Uniqueness of An R-Nu-Generalized Solution of the Dirichlet Problem For the Lame System With a Corner Singularity”, Differ. Equ., 55:6 (2019), 832–840
Rukavishnikov V.A., Rukavishnikova I E., “Comparative Analysis of the Finite Element Methods For the Elasticity Problem With Singularity”, AIP Conference Proceedings, 2116, eds. Simos T., Tsitouras C., Amer Inst Physics, 2019, 450042
V. A. Rukavishnikov, A. V. Rukavishnikov, “New approximate method for solving the Stokes problem in a domain with corner singularity”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 11:1 (2018), 95–108
Rukavishnikov V.A., Rukavishnikova E.I., “the Finite Difference Method For Boundary Value Problem With Singularity”, Finite Difference Methods, Theory and Applications, Lecture Notes in Computer Science, 9045, eds. Dimov I., Farago I., Vulkov L., Springer-Verlag Berlin, 2015, 72–83
Rukavishnikov V.A., Rukavishnikova H.I., “On the Error Estimation of the Finite Element Method for the Boundary Value Problems with Singularity in the Lebesgue Weighted Space”, Numer. Funct. Anal. Optim., 34:12 (2013), 1328–1347
Viktor A. Rukavishnikov, Elena I. Rukavishnikova, Lecture Notes in Computer Science, 8236, Numerical Analysis and Its Applications, 2013, 110
Victor Anatolievich Rukavishnikov, “On Differential Properties Rν-Generalized Solution of the Dirichlet Problem with Coordinated Degeneration of the Input Data”, ISRN Mathematical Analysis, 2011 (2011), 1
Rukavishnikov V.A., “Methods of numerical analysis for boundary value problems with strong singularity”, Russian J. Numer. Anal. Math. Modelling, 24:6 (2009), 565–590

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Sibirskii Zhurnal Vychislitel'noi Matematiki

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