Summary
A common strategy in the numerical integration over ann-dimensional hypercube or simplex, is to consider a regular subdivision of the integration domain intom n subdomains and to approximate the integral over each subdomain by means of a cubature formula. An asymptotic error expansion whenm → ∞ is derived in case of an integrand with homogeneous boundary singularities. The error expansion also copes with the use of different cubature formulas for the boundary subdomains and for the interior subdomains.
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Verlinden, P., Haegemans, A. An error expansion for cubature with an integrand with homogeneous boundary singularities. Numer. Math. 65, 383–406 (1993). https://doi.org/10.1007/BF01385758
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DOI: https://doi.org/10.1007/BF01385758