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arXiv · 2608.28883

A General Superconvergence Result for Cubature on Triangulated Polygonal Domains

Jonah A. Reeger
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Abstract

Cubature rules, which approximate definite integrals as a linear combination of a set of function values, are ubiquitous and necessary for computational methods in the physical sciences. A superconvergence result for cubature rules on polygonal domains is developed, whereby a rule that is exact for all bivariate polynomials of a fixed even degree realize an extra order of convergence under a decrease in the spacing between nodes.

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Jonah A. Reeger. 2026-08-28. A General Superconvergence Result for Cubature on Triangulated Polygonal Domains. https://arxiv.org/abs/2608.28883

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