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Zapiski Nauchnykh Seminarov POMI, 2009, Volume 370, Pages 94–110 (Mi znsl3533)  
This article is cited in 5 scientific papers (total in 5 papers)

Two-sided a posteriori error bounds for electro-magneto static problems

D. Paulya, S. Repinb

a University of Duisburg-Essen, Campus Essen, Faculty for Mathematics, Essen, Germany
b St. Petersburg Department of V. A. Steklov Institute of Mathematics, St. Petersburg, Russia
Full-text PDF (597 kB) Citations (5)
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Abstract: This paper is concerned with the derivation of computable and guaranteed upper and lower bounds of the difference between the exact and the approximate solution of a boundary value problem for static Maxwell equations. Our analysis is based upon purely functional argumentation and does not attract specific properties of an approximation method. Therefore, the estimates derived in the paper at hand are applicable to any approximate solution that belongs to the corresponding energy space. Such estimates (also called error majorants of the functional type) have been derived earlier for elliptic problems [19, 20]. Bibl. – 24 titles.
Key words and phrases: a posteriori error estimatesd of the functional type, Maxwell's boundary value problem, electro-magneto statics.
Received: 25.09.2009
English version:
Journal of Mathematical Sciences (New York), 2010, Volume 166, Issue 1, Pages 53–62
DOI: https://doi.org/10.1007/s10958-010-9844-x
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: English
Citation: D. Pauly, S. Repin, “Two-sided a posteriori error bounds for electro-magneto static problems”, Boundary-value problems of mathematical physics and related problems of function theory. Part 40, Zap. Nauchn. Sem. POMI, 370, POMI, St. Petersburg, 2009, 94–110; J. Math. Sci. (N. Y.), 166:1 (2010), 53–62
Citation in format AMSBIB
\Bibitem{PauRep09}
\by D.~Pauly, S.~Repin
\paper Two-sided a~posteriori error bounds for electro-magneto static problems
\inbook Boundary-value problems of mathematical physics and related problems of function theory. Part~40
\serial Zap. Nauchn. Sem. POMI
\yr 2009
\vol 370
\pages 94--110
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl3533}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2010
\vol 166
\issue 1
\pages 53--62
\crossref{https://doi.org/10.1007/s10958-010-9844-x}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77949295760}
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  • https://www.mathnet.ru/eng/znsl/v370/p94
    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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