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Russia Izhevsk
Section  Mathematics 
Title  Independence of interpolation error estimates by polynomials of $2k+1$ degree on angles in a triangle 
Author(s)  Bazhenov V.S.^{a}, Latypova N.V.^{a} 
Affiliations  Udmurt State University^{a} 
Abstract  The paper considers Birkhofftype trianglebased interpolation of twovariable function by polynomials of $2k+1$ degree by set of two variables. Similar estimates are automatically transferred to error estimates of related finite element method. The approximation error estimates of derivatives for the given finite elements depend only on the decomposition diameter, and do not depend on triangulation angles. We show that obtained approximation error estimates for a function and its partial derivatives are unimprovable. Unimprovability is understood in a following sense: there exists a 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. In this work, a system of specific functions is offered for interpolation conditions. These functions allow to obtain corresponding error estimates for definite partial derivatives. 
Keywords  error of interpolation, piecewise polynomial function, triangulation, finite element method 
UDC  517.518 
MSC  41A05 
DOI  10.20537/vm160202 
Received  29 February 2016 
Language  Russian 
Citation  Bazhenov V.S., Latypova N.V. Independence of interpolation error estimates by polynomials of $2k+1$ degree on angles in a triangle, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2016, vol. 26, issue 2, pp. 160168. 
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