Geodesic
Estimation of the error of calculating the functional containing higher-order derivatives on a triangular grid
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1856-1867

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In the present paper, it is proved that a functional containing second derivatives can be calculated with an error of order $ O (h ^ {4m+1}) $ with a triangular mesh of $h \to 0$ if the piecewise polynomial functions of degree $ 4m+1 $ for $m\geq 1$. For $ n = 2 $ we give an example of the fact that the piecewise quadratic approximation gives the second order of accuracy for calculating the functional for a special kind of triangulation.
Keywords: piecewise polynomial function, approximation of the functional
Mots-clés : triangulation. 
@article{SEMR_2019_16_a119,
     author = {A. A. Klyachin},
     title = {Estimation of the error of calculating the functional containing higher-order derivatives on a triangular grid},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1856--1867},
     publisher = {mathdoc},
     volume = {16},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2019_16_a119/}
}
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A. A. Klyachin. Estimation of the error of calculating the functional containing higher-order derivatives on a triangular grid. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1856-1867. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a119/