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.
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