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Russia Izhevsk
Section  Mathematics 
Title  Independence of interpolation error estimates by fifthdegree polynomials on angles in a triangle 
Author(s)  Latypova N.V.^{a} 
Affiliations  Udmurt State University^{a} 
Abstract  The paper considers several methods of Birkhofftype trianglebased interpolation of twovariable function by fifthdegree 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 fifthdegree polynomials on angles in a triangle, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2012, issue 3, pp. 5364. 
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