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A refined first-order expansion formula in Rn : Application to interpolation and finite element error estimates

Abstract : The aim of this paper is to derive a refined first-order expansion formula in Rn , the goal being to get an optimal reduced remainder, compared to the one obtained by usual Taylor's formula. For a given function, the formula we derived is obtained by introducing a linear combination of the first derivatives, computed at n + 1 equally spaced points. We show how this formula can be applied to two important applications: the interpolation error and the finite elements error estimates. In both cases, we illustrate under which conditions a significant improvement of the errors can be obtained, namely how the use of the refined expansion can reduce the upper bound of error estimates.
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https://hal-cnrs.archives-ouvertes.fr/hal-03832065
Contributor : joel chaska Connect in order to contact the contributor
Submitted on : Thursday, October 27, 2022 - 1:19:21 PM
Last modification on : Sunday, October 30, 2022 - 3:47:39 AM

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  • HAL Id : hal-03832065, version 1

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Joël Chaskalovic, Franck Assous. A refined first-order expansion formula in Rn : Application to interpolation and finite element error estimates. Proceedings of the Royal Society of Edinburgh: Section A, Mathematics, In press. ⟨hal-03832065⟩

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