High-order numerical integration on self-affine sets
<|reference_start|>High-order numerical integration on self-affine sets: 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.<|reference_end|>
@article{joly2024high-order,
    title={High-order numerical integration on self-affine sets},
    author={Patrick Joly and Maryna Kachanovska and Zo"is Moitier},
    journal={arXiv preprint arXiv:2410.00637},
    year={2024},
    archivePrefix={arXiv},
    eprint={2410.00637},
    primaryClass={math.NA cs.NA}
}