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Sib. Zh. Vychisl. Mat., 2009, Volume 12, Number 3, Pages 313–324 (Mi sjvm25)  

This article is cited in 8 scientific papers (total in 8 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
\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
\jour Num. Anal. Appl.
\yr 2009
\vol 2
\issue 3
\pages 250--259

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    This publication is cited in the following articles:
    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  crossref  mathscinet  zmath  isi  elib  scopus
    2. 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  crossref  mathscinet  zmath  isi  elib  scopus
    3. 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  crossref  mathscinet  zmath  isi  scopus
    4. 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  mathnet  crossref  elib
    5. V. A. Rukavishnikov, A. O. Mosolapov, “Vesovoi vektornyi metod konechnykh elementov i ego prilozheniya”, Kompyuternye issledovaniya i modelirovanie, 11:1 (2019), 71–86  mathnet  crossref
    6. 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  mathnet  crossref  elib
    7. 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  crossref  mathscinet  zmath  isi  scopus
    8. 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  crossref  mathscinet  isi  scopus
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