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Russia Izhevsk
Year
2012
Issue
3
Pages
53-64
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Section Mathematics
Title Independence of interpolation error estimates by fifth-degree polynomials on angles in a triangle
Author(-s) Latypova N.V.a
Affiliations Udmurt State Universitya
Abstract The paper considers several methods of Birkhoff-type triangle-based interpolation of two-variable function by fifth-degree polynomials. Similar estimates are automatically transferred to error estimates of related finite element method. The error estimates for the given elements depend only on the decomposition diameter, and do not depend on triangulation angles. We show that the estimates obtained are unimprovable. Unimprovability is understood in a following sense: there exists function from the given class and there exist absolute positive constants independent of triangulation such that for any nondegenerate triangle estimates from below are valid.
Keywords error of interpolation, piecewise polynomial function, triangulation, finite element method
UDC 517.518
MSC 41A05
DOI 10.20537/vm120306
Received 29 March 2012
Language Russian
Citation Latypova N.V. Independence of interpolation error estimates by fifth-degree polynomials on angles in a triangle, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2012, issue 3, pp. 53-64.
References
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  3. Subbotin Yu.N. Dependence of the estimates of approximation by interpolating polynomials of 5-th degree upon geometric properties of triangle, Tr. Inst. Mat. Mekh. Ural. Otd. Ross. Akad. Nauk, 1992, vol. 2, pp. 110-119.
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  8. Latypova N.V. Error of interpolation by piecewise cubic polynomial on triangle, Vestn. Udmurt. Univ. Mat., 2003, pp. 3-18.
  9. Latypova N.V. Error of interpolation by a piecewise parabolic polynomial on a triangle, Vestn. Udmurt. Univ. Mat. Mekh. Komp'yut. Nauki, 2009, no. 3, pp. 91-97.
  10. Latypova N.V. Independence of error estimates of interpolation by cubic polynomials from the angles of a triangle, Tr. Inst. Mat. Mekh. Ural. Otd. Ross. Akad. Nauk, 2011, vol. 17, no 3, pp. 233-241.
  11. Latypova N.V. Independence of interpolation error by fourth-degree polynomials on angles in a triangle, Vestn. Udmurt. Univ. Mat. Mekh. Komp'yut. Nauki, 2011, no. 3, pp. 64-74.
  12. Berezin I.S., Zhidkov N.P. Metody vychislenii (Computing Methods), vol. 1, Moscow: Fizmatgiz, 1962. 464 p.
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