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Article Dans Une Revue Proceedings of the Royal Society of Edinburgh: Section A, Mathematics Année : 2022

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

Franck Assous

Résumé

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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hal-03832065 , version 1 (27-10-2022)

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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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