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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2009, Volume 12, Number 4, Pages 375–388 (Mi sjvm133)  
This article is cited in 6 scientific papers (total in 6 papers)

On using the Lagrange coefficients for a posteriori error estimation

A. K. Alekseeva, I. N. Makhnevb

a Moscow Institute of Physics and Technology, Rocket and Space Corporation "Energia", Korolev, Moscow region
b Moscow Institute of Physics and Technology, Dolgoprudnyi, Moscow region
Full-text PDF (261 kB) Citations (6)
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Abstract: A posteriori error estimation of the goal functional is considered using a differential presentation of a finite difference scheme and adjoint equations. The local approximation error is presented as a Tailor series remainder in the Lagrange form. The field of the Lagrange coefficients is determined by a high accuracy finite difference stencil affecting results of computation. The feasibility of using the Lagrange coefficients for the refining solution and estimation of its uncertainty are considered.
Key words: a posteriori error estimation, postprocessor, adjoint equations.
Received: 25.01.2008
Revised: 02.04.2009
English version:
Numerical Analysis and Applications, 2009, Volume 2, Issue 4, Pages 302–313
DOI: https://doi.org/10.1134/S1995423909040028
Bibliographic databases:
UDC: 533+519.6
Language: Russian
Citation: A. K. Alekseev, I. N. Makhnev, “On using the Lagrange coefficients for a posteriori error estimation”, Sib. Zh. Vychisl. Mat., 12:4 (2009), 375–388; Num. Anal. Appl., 2:4 (2009), 302–313
Citation in format AMSBIB
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\by A.~K.~Alekseev, I.~N.~Makhnev
\paper On using the Lagrange coefficients for a~posteriori error estimation
\jour Sib. Zh. Vychisl. Mat.
\yr 2009
\vol 12
\issue 4
\pages 375--388
\mathnet{http://mi.mathnet.ru/sjvm133}
\transl
\jour Num. Anal. Appl.
\yr 2009
\vol 2
\issue 4
\pages 302--313
\crossref{https://doi.org/10.1134/S1995423909040028}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77952872507}
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  • https://www.mathnet.ru/eng/sjvm133
  • https://www.mathnet.ru/eng/sjvm/v12/i4/p375
    • This publication is cited in the following 6 articles:
    1. Alekseev A.K. Bondarev A.E., “On a Posteriori Error Estimation Using Distances Between Numerical Solutions and Angles Between Truncation Errors”, Math. Comput. Simul., 190 (2021), 892–904  crossref  mathscinet  isi  scopus
    2. A. K. Alekseev, A. E. Bondarev, “On a posteriori estimation of the approximation error norm for an ensemble of independent solutions”, Num. Anal. Appl., 13:3 (2020), 195–206  mathnet  crossref  crossref  isi
    3. Alekseev A.K., Bondarev A.E., Kuvshinnikov A.E., “on Uncertainty Quantification Via the Ensemble of Independent Numerical Solutions”, J. Comput. Sci., 42 (2020), 101114  crossref  mathscinet  isi  scopus
    4. A. K. Alekseev, A. E. Bondarev, “Ispolzovanie ansamblya chislennykh reshenii dlya otsenki pogreshnostei usecheniya i approksimatsii”, Preprinty IPM im. M. V. Keldysha, 2019, 107, 24 pp.  mathnet  crossref
    5. A. K. Alekseev, A. E. Bondarev, A. E. Kuvshinnikov, Lecture Notes in Computer Science, 11540, Computational Science – ICCS 2019, 2019, 315  crossref
    6. M.E. Frolov, “Implementation of error control for solving plane problems in linear elasticity by mixed finite elements”, Comp. Contin. Mech., 7:1 (2014), 73  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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