Simple Formula for Integration of Polynomials on a Simplex

2019/08/19 by Jean Lasserre, Lasserre, Jean
Computer Science · Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Numerical Analysis (math.NA) #cs.NA #math.CA #math.NA

paper · pdf · doi:10.48550/arxiv.1908.06736

To appear in BIT Numerical Mathematics

arxiv created 2020/08/27 · arxiv updated 2020/08/28

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 ξ 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.

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