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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Joly et al. (2024) studied this question.
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