On an integration rule for products of barycentric coordinates over simplexes in Rn

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Abstract

In finite-element computations, one often needs to calculate integrals of products of powers of monomials over simplexes. In this manuscript, we prove a generalisation of the exact integration formula that was reported and proved for two-dimensional simplexes by Holand & Bell in 1969. We extend the proof to n-dimensional simplexes and to simplexes on d-dimensional manifolds in n-dimensional space. The results are used to develop finite-element and boundary-element simulation tools. The proofs of the theorems are based on mathematical induction and coordinate mappings.

Original languageEnglish
Pages (from-to)289-294
Number of pages6
JournalJournal of Computational and Applied Mathematics
Volume330
DOIs
Publication statusPublished - 2018

Keywords

  • Barycentric coordinates
  • Factorisations
  • Finite element methods
  • Integration rule

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