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Ufimsk. Mat. Zh., 2014, Volume 6, Issue 3, Pages 3–16 (Mi ufa249)  

This article is cited in 8 scientific papers (total in 8 papers)

On uniform convergence of piecewise-linear solutions to minimal surface equation

M. A. Gatsunaev, A. A. Klyachin

Volgograd State University, Universitetsky av., 100, 400062, Volgograd, Russia

Abstract: In the paper we consider piecewise-linear solutions of the minimal surface equation over a given triangulation of a polyhedral domain. It is shown that under certain conditions, the gradients of these functions are bounded as the maximal diameter of the triangles of the triangulation tends to zero. It is stressed that this property holds if the piecewise-linear function approximates the area of the graph of a smooth function with a required accuracy. An implication of the obtained properties is the uniform convergence of piecewise linear solutions to the exact solution of the minimal surface equation.

Keywords: piecewise-linear functions, minimal surface equation, the approximation of the area functional.

Full text: PDF file (541 kB)
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English version:
Ufa Mathematical Journal, 2014, 6:3, 3–16 (PDF, 350 kB); https://doi.org/10.13108/2014-6-3-3

Bibliographic databases:

UDC: 517.95
MSC: 35J25, 35J93, 65N30
Received: 11.03.2014

Citation: M. A. Gatsunaev, A. A. Klyachin, “On uniform convergence of piecewise-linear solutions to minimal surface equation”, Ufimsk. Mat. Zh., 6:3 (2014), 3–16; Ufa Math. J., 6:3 (2014), 3–16

Citation in format AMSBIB
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\by M.~A.~Gatsunaev, A.~A.~Klyachin
\paper On uniform convergence of piecewise-linear solutions to minimal surface equation
\jour Ufimsk. Mat. Zh.
\yr 2014
\vol 6
\issue 3
\pages 3--16
\mathnet{http://mi.mathnet.ru/ufa249}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3427546}
\elib{http://elibrary.ru/item.asp?id=22370772}
\transl
\jour Ufa Math. J.
\yr 2014
\vol 6
\issue 3
\pages 3--16
\crossref{https://doi.org/10.13108/2014-6-3-3}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84928177706}


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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. A. A. Klyachin, “On the uniform convergence of piecewise linear solutions to the equilibrium capillary surface equation”, J. Appl. Industr. Math., 9:3 (2015), 381–391  mathnet  crossref  crossref  mathscinet  elib
    2. A. A. Klyachin, “Otsenka pogreshnosti vychisleniya integralnykh funktsionalov s pomoschyu kusochno-lineinykh funktsii”, Vestn. Volgogr. gos. un-ta. Ser. 1, Mat. Fiz., 2015, no. 1(26), 6–12  mathnet  crossref
    3. V. A. Klyachin, E. G. Grigoreva, “Chislennoe issledovanie ustoichivosti ravnovesnykh poverkhnostei s ispolzovaniem paketa NumPy”, Vestn. Volgogr. gos. un-ta. Ser. 1, Mat. Fiz., 2015, no. 2(27), 17–30  mathnet  crossref
    4. A. A. Klyachin, A. Yu. Belenikina, “Triangulyatsiya prostranstvennykh elementarnykh oblastei”, Vestn. Volgogr. gos. un-ta. Ser. 1, Mat. Fiz., 2015, no. 4(29), 6–12  mathnet  crossref
    5. A. A. Klyachin, I. V. Truhlyaeva, “On convergence of polynomial solutions of minimal surface”, Ufa Math. J., 8:1 (2016), 68–78  mathnet  crossref  isi  elib
    6. A. A. Klyachin, A. G. Panchenko, “Modelirovanie minimalnykh triangulirovannykh poverkhnostei: otsenka pogreshnosti vychisleniya ploschadi pri proektirovanii sooruzhenii”, Vestn. Volgogr. gos. un-ta. Ser. 1, Mat. Fiz., 2016, no. 3(34), 73–83  mathnet  crossref
    7. I. V. Trukhlyaeva, “O skhodimosti polinomialnykh priblizhennykh reshenii uravneniya minimalnoi poverkhnosti”, Vestn. Volgogr. gos. un-ta. Ser. 1, Mat. Fiz., 2016, no. 5(36), 124–139  mathnet  crossref
    8. E. G. Grigoreva, V. A. Klyachin, A. A. Klyachin, “Universalnyi programmnyi kompleks dlya resheniya mnogomernykh variatsionnykh zadach”, Vestn. Volgogr. gos. un-ta. Ser. 1, Mat. Fiz., 2017, no. 2(39), 39–55  mathnet
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