English

Cheap and stable quadrature on polyhedral elements

Numerical Analysis 2025-02-06 v1 Numerical Analysis

Abstract

We discuss a cheap tetrahedra-free approach to the numerical integration of polynomials on polyhedral elements, based on hyperinterpolation in a bounding box and Chebyshev moment computation via the divergence theorem. No conditioning issues arise, since no matrix factorization or inversion is needed. The resulting quadrature formula is theoretically stable even in the presence of some negative weights.

Keywords

Cite

@article{arxiv.2502.03446,
  title  = {Cheap and stable quadrature on polyhedral elements},
  author = {Alvise Sommariva and Marco Vianello},
  journal= {arXiv preprint arXiv:2502.03446},
  year   = {2025}
}
R2 v1 2026-06-28T21:33:51.393Z