High-order numerical integration on self-affine sets - Inria - Institut national de recherche en sciences et technologies du numérique
Pré-Publication, Document De Travail Année : 2024

High-order numerical integration on self-affine sets

Résumé

We construct an interpolatory high-order cubature rule to compute integrals of smooth functions over self-affine sets with respect to an invariant measure. The main difficulty is the computation of the cubature weights, which we characterize algebraically, by exploiting a self-similarity property of the integral. We propose an \( h \)-version and a \( p \)-version of the cubature, present an error analysis and conduct numerical experiments.
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Dates et versions

hal-04711030 , version 1 (26-09-2024)

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  • HAL Id : hal-04711030 , version 1

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Patrick Joly, Maryna Kachanovska, Zoïs Moitier. High-order numerical integration on self-affine sets. 2024. ⟨hal-04711030⟩
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