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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2005, Volume 11, Number 2, Pages 47–52
(Mi timm188)
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This article is cited in 10 scientific papers (total in 10 papers)
A method of Hermite interpolation by polynomials of the third degree on a triangle
N. V. Baidakova
Abstract:
As a rule, in constructing triangular finite elements of Hermite or Birkhoff type, the denominators of
interpolation error bounds contain the sine of the minimum angle in the triangle. This leads to the necessity
to impose some restrictions on the triangulation of the domain. Excluding the paper by Yu. N. Subbotin
published in the present issue, the author does not know any description of the cases where the minimum
angle is absent in the estimates of all derivatives up to order $n$ inclusive when a function is interpolated by
Hermite or Birkhoff's polynomial of degree $n$. In this paper, a new method of Hermite interpolation of a function in two variables on a triangle by polynomials of degree 3 is suggested. For the proposed method, the sine of the minimum angle is absent in the denominators of error bounds for any derivatives of the function
up to the third order, which makes it possible to weaken our requirements on the triangulation.
Received: 27.12.2004
Citation:
N. V. Baidakova, “A method of Hermite interpolation by polynomials of the third degree on a triangle”, Function theory, Trudy Inst. Mat. i Mekh. UrO RAN, 11, no. 2, 2005, 47–52; Proc. Steklov Inst. Math. (Suppl.), 2005no. , suppl. 2, S49–S55
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https://www.mathnet.ru/eng/timm188 https://www.mathnet.ru/eng/timm/v11/i2/p47
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Abstract page: | 563 | Full-text PDF : | 199 | References: | 55 |
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