Geodesic
Approximation of the Derivatives of a Function in Lagrange Interpolation on Low-Dimensional Simplices
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function Spaces, Approximation Theory, and Related Problems of Analysis, Tome 312 (2021), pp. 272-281

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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.
Mots-clés : multidimensional interpolation
Keywords: finite element method. 
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     author = {Yu. N. Subbotin and N. V. Baidakova},
     title = {Approximation of the {Derivatives} of a {Function} in {Lagrange} {Interpolation} on {Low-Dimensional} {Simplices}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {272--281},
     publisher = {mathdoc},
     volume = {312},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2021_312_a16/}
}
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Yu. N. Subbotin; N. V. Baidakova. Approximation of the Derivatives of a Function in Lagrange Interpolation on Low-Dimensional Simplices. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function Spaces, Approximation Theory, and Related Problems of Analysis, Tome 312 (2021), pp. 272-281. http://geodesic.mathdoc.fr/item/TM_2021_312_a16/