Geodesic
Independence of interpolation error estimates by fourth-degree polynomials on angles in a triangle
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 3 (2011), pp. 64-74 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper considers two methods of Birkhoff-type triangle-based interpolation of two-variable function by fourth-degree polynomials for the finite element method. The error estimates for the given elements depend only on the decomposition diameter, and do not depend on triangulation angles. We show that the estimates obtained are unimprovable.
Mots-clés : error of interpolation, triangulation
Keywords: piecewise polynomial function, finite element method. 
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     title = {Independence of interpolation error estimates by fourth-degree polynomials on angles in a~triangle},
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N. V. Latypova. Independence of interpolation error estimates by fourth-degree polynomials on angles in a triangle. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 3 (2011), pp. 64-74. http://geodesic.mathdoc.fr/item/VUU_2011_3_a5/

[1] Ciarlet P. G., Raviart P. A., “General Lagrange and Hermite interpolation in $R^n$ with applications to finite element methods”, Arch. Rat. Mech. and Anal., 46:3 (1972), 177–199 | DOI | MR | Zbl

[2] Subbotin Yu. N., “Mnogomernaya kratnaya polinomialnaya interpolyatsiya”, Metody approksimatsii i interpolyatsii, cb., Novosibirsk, 1981, 148–152 | MR

[3] Subbotin Yu. N., “Zavisimost otsenok approksimatsii interpolyatsionnymi polinomami pyatoi stepeni ot geometricheskikh kharakteristik treugolnika”, Tr. IMM UrO RAN, 2, 1992, 110–119 | MR | Zbl

[4] Subbotin Yu. N., “A New Cubic Element in the FEM”, Proceeding of the Steklov Institute of Mathematics, 2005, S176–S187 | MR | Zbl

[5] Baidakova N. V., “On some interpolation process by polynomials of degree $4m+1$ on the triangle”, Russian Journal of numerical analysis and mathematical modelling, 14:2 (1999), 87–107 | DOI | MR | Zbl

[6] Baidakova N. V., “A Method of Hermite interpolation by polynomials of the third degree on a triangle”, Proceeding of the Steklov Institute of Mathematics, 2005, S49–S55 | MR | Zbl

[7] Latypova N. V., “Pogreshnost approksimatsii mnogochlenami stepeni $4k+3$ na treugolnike”, Trudy Mezhdunarodnoi shkoly S. B. Stechkina po teorii funktsii, cb., UrO RAN, Ekaterinburg, 1999, 128–137

[8] Latypova N. V., “Error estimates of approximation by polynomials of degree $4k+3$ on the triangle”, Proceeding of the Steklov Institute of Mathematics, 2002, S190–S213 | MR | Zbl

[9] Latypova N. V., “Pogreshnost kusochno-kubicheskoi interpolyatsii na treugolnike”, Vestnik Udmurtskogo universiteta. Matematika, 2003, 3–18

[10] Latypova N. V., “Pogreshnost kusochno-parabolicheskoi interpolyatsii na treugolnike”, Vestnik Udmurtskogo universiteta. Matematika. Mekhanika. Kompyuternye nauki, 2009, no. 3, 91–97

[11] Berezin I. S., Zhidkov N. P., Metody vychislenii, uchebnik dlya vuzov, v. 1, Fizmatgiz, M., 1962, 464 pp. | MR