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Sib. Zh. Vychisl. Mat., 2016, Volume 19, Number 1, Pages 47–59 (Mi sjvm601)  

This article is cited in 3 scientific papers (total in 3 papers)

Convergence of the adapting grid method of Bakhvalov's type for singularly perturbed boundary value problems

I. A. Blatov, E. V. Kitaeva

Povolzhskiy State University of Telecommunications and Informatics, 23 Lev Tolstoi str., Samara, 443010, Russia

Abstract: We consider the Galerkin finite element method for non-self-adjoint boundary value problems on Bakhvalov's grids. Using the Galerkin projections method the convergence of a sequence of computational grids with an unknown boundary of the boundary layer has been proved. Numerical examples are presented.

Key words: singularly perturbed boundary value problem, Galerkin projection, Bakhvalov's grid, adaptation algorithms.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-01-06584


DOI: https://doi.org/10.15372/SJNM20160104

Full text: PDF file (435 kB)
References: PDF file   HTML file

English version:
Numerical Analysis and Applications, 2016, 9:1, 34–44

Bibliographic databases:

UDC: 519.6
Received: 24.02.2015
Revised: 18.05.2015

Citation: I. A. Blatov, E. V. Kitaeva, “Convergence of the adapting grid method of Bakhvalov's type for singularly perturbed boundary value problems”, Sib. Zh. Vychisl. Mat., 19:1 (2016), 47–59; Num. Anal. Appl., 9:1 (2016), 34–44

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. I. A. Blatov, A. I. Zadorin, E. V. Kitaeva, “Cubic spline interpolation of functions with high gradients in boundary layers”, Comput. Math. Math. Phys., 57:1 (2017), 7–25  mathnet  crossref  crossref  isi  elib
    2. I. A. Blatov, A. I. Zadorin, E. V. Kitaeva, “About the uniform convergence of parabolic spline interpolation on the class of functions with large gradients in the boundary layer”, Num. Anal. Appl., 10:2 (2017), 108–119  mathnet  crossref  crossref  isi  elib
    3. I. A. Blatov, A. I. Zadorin, E. V. Kitaeva, “On the parameter-uniform convergence of exponential spline interpolation in the presence of a boundary layer”, Comput. Math. Math. Phys., 58:3 (2018), 348–363  mathnet  crossref  crossref  isi  elib
  • Sibirskii Zhurnal Vychislitel'noi Matematiki
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