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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2011, Number 5, Pages 88–92 (Mi ivm7309)  
Brief communications

Schemes of the finite element method with separation of singularity for a two-point boundary-value problem of the 4th order with degenerate coefficients

A. A. Sobolev, M. R. Timerbaev

Chair of Computational Mathematics, Kazan (Volga Region) Federal University, Kazan, Russia
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Abstract: In this paper we construct a high accuracy variant of the finite element method for an ordinary differential equation of the fourth order whose coefficients are degenerate on the boundary. The proposed technique is based on the multiplicative and additive-multiplicative separation of singularity. We prove that the convergence rate of the proposed technique is optimal in a given class of smoothness of right-hand sides.
Keywords: two-point boundary value problem, finite element schemes, weight function spaces, multiplicative and additive-multiplicative separation of singularity.
Presented by the member of Editorial Board: R. Z. Dautov
Received: 25.11.2010
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2011, Volume 55, Issue 5, Pages 74–77
DOI: https://doi.org/10.3103/S1066369X11050136
Bibliographic databases:
Document Type: Article
UDC: 519.6
Language: Russian
Citation: A. A. Sobolev, M. R. Timerbaev, “Schemes of the finite element method with separation of singularity for a two-point boundary-value problem of the 4th order with degenerate coefficients”, Izv. Vyssh. Uchebn. Zaved. Mat., 2011, no. 5, 88–92; Russian Math. (Iz. VUZ), 55:5 (2011), 74–77
Citation in format AMSBIB
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\by A.~A.~Sobolev, M.~R.~Timerbaev
\paper Schemes of the finite element method with separation of singularity for a~two-point boundary-value problem of the 4th order with degenerate coefficients
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2011
\issue 5
\pages 88--92
\mathnet{http://mi.mathnet.ru/ivm7309}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2920095}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2011
\vol 55
\issue 5
\pages 74--77
\crossref{https://doi.org/10.3103/S1066369X11050136}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-80051627407}
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