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Sibirskii Zhurnal Industrial'noi Matematiki, 2014, Volume 17, Number 2, Pages 137–148 (Mi sjim840)  
This article is cited in 4 scientific papers (total in 4 papers)

Convergence of the finite element method for elliptic equations with strong degeneration

M. V. Urevab

a Institute of Computational Mathematics and Mathematical Geophysics SB RAS, 6 Lavrent'ev av., 630090 Novosibirsk
b Novosibirsk State University, 2 Pirogova st., 630090 Novosibirsk
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Abstract: We consider the questions of numerical solution by the finite element method (FEM) for the first boundary value problem for an elliptic equation with degeneration on a part of the boundary. We pose the weak and strong variational statements in the function spaces with compatible weights that correspond to the problem. Using the method of the multiplicative separation of singularity for the finite element method that utilizes piecewise linear elements, we prove that the convergence of the approximate solutions to the exact solution in the weighted norm is no worse than in the case of an elliptic equation without degeneracy.
Keywords: elliptic equation with degeneracy, weighted Sobolev space, multiplicative separation of singularity, finite element method, convergence.
Received: 10.01.2014
English version:
Journal of Applied and Industrial Mathematics, 2014, Volume 8, Issue 3, Pages 411–421
DOI: https://doi.org/10.1134/S1990478914030144
Bibliographic databases:
Document Type: Article
UDC: 519.632
Language: Russian
Citation: M. V. Urev, “Convergence of the finite element method for elliptic equations with strong degeneration”, Sib. Zh. Ind. Mat., 17:2 (2014), 137–148; J. Appl. Industr. Math., 8:3 (2014), 411–421
Citation in format AMSBIB
\Bibitem{Ure14}
\by M.~V.~Urev
\paper Convergence of the finite element method for elliptic equations with strong degeneration
\jour Sib. Zh. Ind. Mat.
\yr 2014
\vol 17
\issue 2
\pages 137--148
\mathnet{http://mi.mathnet.ru/sjim840}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=3379247}
\transl
\jour J. Appl. Industr. Math.
\yr 2014
\vol 8
\issue 3
\pages 411--421
\crossref{https://doi.org/10.1134/S1990478914030144}
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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