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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2016, Volume 56, Number 7, Pages 1323–1334
DOI: https://doi.org/10.7868/S0044466916070061 (Mi zvmmf10422) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Conditional $\varepsilon$-uniform boundedness of Galerkin projectors and convergence of an adaptive mesh method as applied to singularly perturbed boundary value problems

I. A. Blatov, N. V. Dobrobog, E. V. Kitaeva

Volga State University of Telecommunications and Informatics, Moskovskoe sh. 77, Samara, 443010, Russia
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DOI: https://doi.org/10.7868/S0044466916070061
Abstract: The Galerkin finite element method is applied to nonself-adjoint singularly perturbed boundary value problems on Shishkin meshes. The Galerkin projection method is used to obtain conditionally $\varepsilon$-uniform a priori error estimates and to prove the convergence of a sequence of meshes in the case of an unknown boundary layer edge.
Key words: singularly perturbed boundary value problem, Galerkin projector, Shishkin mesh, adaptive algorithms.
Funding agency Grant number
Russian Foundation for Basic Research 15-01-06584_а
Received: 17.11.2014
Revised: 06.10.2015
English version:
Computational Mathematics and Mathematical Physics, 2016, Volume 56, Issue 7, Pages 1293–1304
DOI: https://doi.org/10.1134/S096554251607006X
Bibliographic databases:
Document Type: Article
UDC: 519.63
Language: Russian
Citation: I. A. Blatov, N. V. Dobrobog, E. V. Kitaeva, “Conditional $\varepsilon$-uniform boundedness of Galerkin projectors and convergence of an adaptive mesh method as applied to singularly perturbed boundary value problems”, Zh. Vychisl. Mat. Mat. Fiz., 56:7 (2016), 1323–1334; Comput. Math. Math. Phys., 56:7 (2016), 1293–1304
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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