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Russia Izhevsk
Section  Mathematics 
Title  Error of interpolation by sixthdegree polynomials on a triangle 
Author(s)  Latypova N.V.^{a} 
Affiliations  Udmurt State University^{a} 
Abstract  The paper considers Birkhofftype trianglebased interpolation to a twovariable function by sixthdegree 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. 
Keywords  error of interpolation, piecewise polynomial function, triangulation, finite element method 
UDC  517.518 
MSC  41A05 
DOI  10.20537/vm130408 
Received  19 October 2013 
Language  Russian 
Citation  Latypova N.V. Error of interpolation by sixthdegree polynomials on a triangle, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2013, issue 4, pp. 7987. 
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