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Zh. Vychisl. Mat. Mat. Fiz., 2016, Volume 56, Number 7, Pages 1323–1334 (Mi zvmmf10422)  

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

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


DOI: https://doi.org/10.7868/S0044466916070061

Full text: PDF file (225 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2016, 56:7, 1293–1304

Bibliographic databases:

UDC: 519.63
Received: 17.11.2014
Revised: 06.10.2015

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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  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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