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Sib. Zh. Vychisl. Mat., 2001, Volume 4, Number 3, Pages 201–228 (Mi sjvm396)  

This article is cited in 6 scientific papers (total in 6 papers)

The use of singular functions in the $h$-$p$ version of the finite element method for a Dirichlet problem with degeneration of the input data

A. Yu. Bespalov, V. A. Rukavishnikov

Computing Center, Far-Eastern Branch, Russian Academy of Sciences, Khabarovsk, Russia

Abstract: The paper is devoted to a Dirichlet problem for a second-order non-self-adjoint elliptic equation with a strong singularity of the solution caused by a coordinated degeneration of input data at boundary points of a two-dimensional domain. The h-p version of the finite element method is used to approximate this problem. We introduce a finite element space with a singular basis that depends on the space to which the solution to the problem belongs. An exponential convergence rate in the norm of a weighted Sobolev space is proved.

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Bibliographic databases:
UDC: 519.632
Received: 30.11.2000
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Citation: A. Yu. Bespalov, V. A. Rukavishnikov, “The use of singular functions in the $h$-$p$ version of the finite element method for a Dirichlet problem with degeneration of the input data”, Sib. Zh. Vychisl. Mat., 4:3 (2001), 201–228

Citation in format AMSBIB
\Bibitem{BesRuk01}
\by A.~Yu.~Bespalov, V.~A.~Rukavishnikov
\paper The use of singular functions in the $h$-$p$ version of the finite element method for a Dirichlet problem with degeneration of the input data
\jour Sib. Zh. Vychisl. Mat.
\yr 2001
\vol 4
\issue 3
\pages 201--228
\mathnet{http://mi.mathnet.ru/sjvm396}
\zmath{https://zbmath.org/?q=an:0987.65118}


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

    This publication is cited in the following articles:
    1. Bespalov A., “Orthogonal Systems of Singular Functions and Numerical Treatment of Problems with Degeneration of Data”, Adv. Comput. Math., 19:1-3 (2003), 159–182  crossref  mathscinet  zmath  isi  scopus
    2. E. V. Kashuba, V. A. Rukavishnikov, “On the $p$-version of the finite element method for the boundary value problem with singularity”, Sib. zhurn. vychisl. matem., 8:1 (2005), 31–42  mathnet  zmath
    3. Rukavishnikov V.A., Kuznetsova E.V., “Coercive estimate for a boundary value problem with noncoordinated degeneration of the data”, Differ. Equ., 43:4 (2007), 550–560  crossref  mathscinet  zmath  isi  elib  elib  scopus
    4. Arroyo D., Bespalov A., Heuer N., “On the Finite Element Method for Elliptic Problems with Degenerate and Singular Coefficients”, Math. Comput., 76:258 (2007), 509–537  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    5. V. A. Rukavishnikov, E. V. Kuznetsova, “A scheme of a finite element method for boundary value problems with non-coordinated degeneration of input data”, Num. Anal. Appl., 2:3 (2009), 250–259  mathnet  crossref
    6. Rukavishnikov V.A., “Methods of Numerical Analysis for Boundary Value Problems with Strong Singularity”, Russ. J. Numer. Anal. Math. Model, 24:6 (2009), 565–590  crossref  mathscinet  zmath  isi  elib  scopus
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