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Russia Izhevsk
Year
2016
Volume
26
Issue
2
Pages
160-168
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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 Universitya
Abstract The paper considers Birkhoff-type triangle-based interpolation of two-variable 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. 160-168.
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