Summary
This paper is devoted to study the Hermite interpolation error in an open subset of ℝn.
It follows a previous work of Arcangeli and Gout [1]. Like this one, it is based principally on the paper of Ciarlet and Raviart [7].
We obtain two kinds of the Hermite interpolation error, the first from the Hermite interpolation polynomial, the other from approximation method using the Taylor polynomial.
Finally in the last part we study some numerical examples concerning straight finite element methods: in the first and second examples, we use finite elements which are included in the affine theory, but it is not the case in the last example. However, in this case, it is possible to refer to the affine theory by the way of particular study (cf. Argyris et al. [2]; Ciarlet [6]; ciarlet and Raviart [7]; Raviart [11]).
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References
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Gout, J.L. Estimation de l'erreur d'interpolation d'Hermite dans ℝn . Numer. Math. 28, 407–429 (1977). https://doi.org/10.1007/BF01404344
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DOI: https://doi.org/10.1007/BF01404344