Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Zh. Vychisl. Mat. Mat. Fiz.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Zh. Vychisl. Mat. Mat. Fiz., 2020, Volume 60, Number 11, Pages 1815–1822 (Mi zvmmf11154)  

General numerical methods

A note on a posteriori error bounds for numerical solutions of elliptic equations with a piecewise constant reaction coefficient having large jumps

V. G. Korneev

St. Petersburg State University, St. Petersburg, 199034 Russia

Abstract: We have derived guaranteed, robust, and fully computable a posteriori error bounds for approximate solutions of the equation $\Delta \Delta u + {{\Bbbk }^{2}}u = f$, where the coefficient $\Bbbk \geqslant 0$ is a constant in each subdomain (finite element) and chaotically varies between subdomains in a sufficiently wide range. For finite element solutions, these bounds are robust with respect to $\Bbbk \in [0,{c}{{{h}}^{{ - 2}}}]$, $c={const}$ , and possess some other good features. The coefficients in front of two typical norms on their right-hand sides are only insignificantly worse than those obtained earlier for $\Bbbk \equiv {const}{.}$ The bounds can be calculated without resorting to the equilibration procedures, and they are sharp for at least low-order methods. The derivation technique used in this paper is similar to the one used in our preceding papers (2017–2019) for obtaining a posteriori error bounds that are not improvable in the order of accuracy.

Key words: a posteriori error bounds, singularly perturbed fourth-order elliptic equations, piecewise constant reaction coefficient, finite element method, sharp bounds.

DOI: https://doi.org/10.31857/S0044466920110071


English version:
Computational Mathematics and Mathematical Physics, 2020, 60:11, 1754–1760

Bibliographic databases:

UDC: 519.632.4
Received: 23.10.2019
Revised: 28.05.2020
Accepted:07.07.2020

Citation: V. G. Korneev, “A note on a posteriori error bounds for numerical solutions of elliptic equations with a piecewise constant reaction coefficient having large jumps”, Zh. Vychisl. Mat. Mat. Fiz., 60:11 (2020), 1815–1822; Comput. Math. Math. Phys., 60:11 (2020), 1754–1760

Citation in format AMSBIB
\Bibitem{Kor20}
\by V.~G.~Korneev
\paper A note on a posteriori error bounds for numerical solutions of elliptic equations with a piecewise constant reaction coefficient having large jumps
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2020
\vol 60
\issue 11
\pages 1815--1822
\mathnet{http://mi.mathnet.ru/zvmmf11154}
\crossref{https://doi.org/10.31857/S0044466920110071}
\elib{https://elibrary.ru/item.asp?id=44038901}
\transl
\jour Comput. Math. Math. Phys.
\yr 2020
\vol 60
\issue 11
\pages 1754--1760
\crossref{https://doi.org/10.1134/S096554252011007X}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=WOS:000596808500002}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85097312368}


Linking options:
  • http://mi.mathnet.ru/eng/zvmmf11154
  • http://mi.mathnet.ru/eng/zvmmf/v60/i11/p1815

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
    Number of views:
    This page:10

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021