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This article is cited in 10 scientific papers (total in 10 papers)
A scheme of a finite element method for boundary value problems with non-coordinated degeneration of input data
V. A. Rukavishnikova, E. V. Kuznetsovab
a Computer Centre Far-Eastern Branch of RAS
b Far Eastern State Transport University
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 $R_{\nu}$-generalized solution in the weight set $W^1_{2,\nu^*+\beta/2+1}(\Omega,\delta)$ is investigated, the estimation of finite element approximations is established.
Key words:
non-coordinated degeneration of input data, $R_{\nu}$-generalized solution, singularity of a solution, finite element method.
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English version:
Numerical Analysis and Applications, 2009, 2:3, 250–259
UDC:
519.632
Received: 14.11.2007
Revised: 21.07.2008
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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\by V.~A.~Rukavishnikov, E.~V.~Kuznetsova
\paper A~scheme of a~finite element method for boundary value problems with non-coordinated degeneration of input data
\jour Sib. Zh. Vychisl. Mat.
\yr 2009
\vol 12
\issue 3
\pages 313--324
\mathnet{http://mi.mathnet.ru/sjvm25}
\transl
\jour Num. Anal. Appl.
\yr 2009
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\issue 3
\pages 250--259
\crossref{https://doi.org/10.1134/S1995423909030069}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-71449085036}
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http://mi.mathnet.ru/eng/sjvm25 http://mi.mathnet.ru/eng/sjvm/v12/i3/p313
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This publication is cited in the following articles:
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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
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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
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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
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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
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V. A. Rukavishnikov, A. O. Mosolapov, “Vesovoi vektornyi metod konechnykh elementov i ego prilozheniya”, Kompyuternye issledovaniya i modelirovanie, 11:1 (2019), 71–86
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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
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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
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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
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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
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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
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