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This article is cited in 1 scientific paper (total in 1 paper)
Approximation of the Derivatives of a Function in Lagrange Interpolation on Low-Dimensional Simplices
Yu. N. Subbotina, N. V. Baidakovaab a N. N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg, 620990 Russia
b Ural Federal University named after the First President of Russia B. N. Yeltsin, ul. Mira 19, Yekaterinburg, 620002 Russia
Abstract:
We address the problem of approximating the derivatives of a differentiable function of $m$ variables ($m=3,4$) by the derivatives of a polynomial on an $m$-simplex for the standard method of interpolation by Lagrange polynomials at the points of a uniform grid on this simplex. For the error of approximation of these derivatives by the derivatives of the interpolation polynomial, we obtain upper bounds expressed in terms of new geometric characteristics of the simplex. The proposed characteristics of the simplex are clear and easy to calculate.
Keywords:
multidimensional interpolation, finite element method.
Received: July 1, 2020 Revised: August 31, 2020 Accepted: October 4, 2020
Citation:
Yu. N. Subbotin, N. V. Baidakova, “Approximation of the Derivatives of a Function in Lagrange Interpolation on Low-Dimensional Simplices”, Function Spaces, Approximation Theory, and Related Problems of Analysis, Collected papers. In commemoration of the 115th anniversary of Academician Sergei Mikhailovich Nikol'skii, Trudy Mat. Inst. Steklova, 312, Steklov Math. Inst., Moscow, 2021, 272–281; Proc. Steklov Inst. Math., 312 (2021), 261–269
Linking options:
https://www.mathnet.ru/eng/tm4154https://doi.org/10.4213/tm4154 https://www.mathnet.ru/eng/tm/v312/p272
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