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Zap. Nauchn. Sem. POMI, 2007, Volume 348, Pages 127–146 (Mi znsl64)  

This article is cited in 2 scientific papers (total in 2 papers)

Functional a posteriori error estimates for the reaction-convection-diffusion problem

S. Nicaisea, S. I. Repinb

a Université de Valenciennes et du Hainaut-Cambrésis
b St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

Abstract: In this paper, a general form of functional type a posteriori error estimates for linear reaction-convection-diffusion problems is presented. It is derived by purely functional arguments without attracting specific properties of the approximation method. The estimate provides a guaranteed upper bound of the difference between the exact solution and any conforming approximation from the energy functional class. It is also proved that the derived error majorants give computable quantities which are equivalent to the error evaluated in the energy and combined primal-dual norms.

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English version:
Journal of Mathematical Sciences (New York), 2008, 152:5, 690–701

UDC: 517
Received: 14.05.2007
Language: English

Citation: S. Nicaise, S. I. Repin, “Functional a posteriori error estimates for the reaction-convection-diffusion problem”, Boundary-value problems of mathematical physics and related problems of function theory. Part 38, Zap. Nauchn. Sem. POMI, 348, POMI, St. Petersburg, 2007, 127–146; J. Math. Sci. (N. Y.), 152:5 (2008), 690–701

Citation in format AMSBIB
\Bibitem{NicRep07}
\by S.~Nicaise, S.~I.~Repin
\paper Functional a posteriori error estimates for the
reaction-convection-diffusion problem
\inbook Boundary-value problems of mathematical physics and related problems of function theory. Part~38
\serial Zap. Nauchn. Sem. POMI
\yr 2007
\vol 348
\pages 127--146
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl64}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2008
\vol 152
\issue 5
\pages 690--701
\crossref{https://doi.org/10.1007/s10958-008-9092-5}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-51749094596}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Repin S., “A posteriori error estimation methods for partial differential equations”, Lectures on Advanced Computational Methods in Mechanics, Radon Series on Computational and Applied Mathematics, 1, 2007, 161–226  mathscinet  zmath  isi
    2. Cochez-Dhondt S., Nicaise S., Repin S., “A Posteriori Error Estimates for Finite Volume Approximations”, Mathematical Modelling of Natural Phenomena, 4:1 (2009), 106–122  crossref  mathscinet  zmath  isi  scopus
  • Записки научных семинаров ПОМИ
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