High-order numerical integration on self-affine sets
Abstract
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.
Domains
Numerical Analysis [math.NA]Origin | Files produced by the author(s) |
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