Simple Formula for Integration of Polynomials on a Simplex
Numerical Analysis
2020-08-28 v2 Numerical Analysis
Classical Analysis and ODEs
Abstract
We show that integrating a polynomial of degree t on an arbitrary simplex (with respect to Lebesgue measure) reduces to evaluating t homogeneous polynomials of degree j = 1, 2,. .. , t, each at a unique point j of the simplex. This new and very simple formula can be exploited in finite (and extended finite) element methods, as well as in other applications where such integrals are needed.
Cite
@article{arxiv.1908.06736,
title = {Simple Formula for Integration of Polynomials on a Simplex},
author = {Jean Lasserre},
journal= {arXiv preprint arXiv:1908.06736},
year = {2020}
}
Comments
To appear in BIT Numerical Mathematics