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arXiv · 2310.19483

Enhancing Interpolation and Approximation Error Estimates Using a Novel Taylor-like Formula

Joel Chaskalovic·Franck Assous
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Abstract

In this paper, we present an approach to enhance interpolation and approximation error estimates. Based on a previously derived first-order Taylor-like formula, we demonstrate its applicability in improving the $P_1$-interpolation error estimate. Following the same principles, we also develop a novel numerical scheme for the heat equation that yields a better error estimate compared to the classical implicit finite differences scheme.

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Joel Chaskalovic, Franck Assous. 2023-10-30. Enhancing Interpolation and Approximation Error Estimates Using a Novel Taylor-like Formula. https://arxiv.org/abs/2310.19483

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