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Section
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Mathematics
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Title
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Error of interpolation by sixth-degree polynomials on a triangle
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Author(-s)
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Latypova N.V.a
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Affiliations
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Udmurt State Universitya
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Abstract
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The paper considers Birkhoff-type triangle-based interpolation to a two-variable function by sixth-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 estimates from below are valid for any nondegenerate triangle.
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Keywords
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error of interpolation, piecewise polynomial function, triangulation, finite element method
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UDC
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517.518
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MSC
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41A05
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DOI
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10.20537/vm130408
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Received
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19 October 2013
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Language
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Russian
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Citation
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Latypova N.V. Error of interpolation by sixth-degree polynomials on a triangle, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2013, issue 4, pp. 79-87.
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References
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- 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.
- 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.
- Latypova N.V. Independence of interpolation error estimates by fourth-degree polynomials on angles in a triangle, Vestn. Udmurt. Univ. Mat. Mekh. Komp'yut. Nauki, 2011, no. 3, pp. 64-74.
- Latypova N.V. Independence of interpolation error estimates by fifth-degree polynomials on angles in a triangle, Vestn. Udmurt. Univ. Mat. Mekh. Komp'yut. Nauki, 2012, no. 3, pp. 53-64.
- Berezin I.S., Zhidkov N.P. Metody vychislenii (Computing Methods), vol. 1, Moscow: Fizmatgiz, 1962, 464 p.
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Full text
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