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SIMPLE FORMULA FOR INTEGRATION OF POLYNOMIALS ON A SIMPLEX

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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https://hal.laas.fr/hal-02266692
Contributor : Jean Bernard Lasserre <>
Submitted on : Wednesday, August 12, 2020 - 10:08:16 PM
Last modification on : Wednesday, June 9, 2021 - 10:00:20 AM

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Jean Lasserre. SIMPLE FORMULA FOR INTEGRATION OF POLYNOMIALS ON A SIMPLEX. BIT Numerical Mathematics, Springer Verlag, 2021, 61, pp.523--533. ⟨10.1007/s10543-020-00828-x⟩. ⟨hal-02266692v2⟩

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