Displaying similar documents to “Some applications and numerical methods for orthogonal polynomials”

Integration of polynomials

Paweł Szeptycki (2004)

Applicationes Mathematicae

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We prove that the only functions for which certain standard numerical integration formulas are exact are polynomials.

Numerical integration for high order pyramidal finite elements

Nilima Nigam, Joel Phillips (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We examine the effect of numerical integration on the accuracy of high order conforming pyramidal finite element methods. Non-smooth shape functions are indispensable to the construction of pyramidal elements, and this means the conventional treatment of numerical integration, which requires that the finite element approximation space is piecewise polynomial, cannot be applied. We develop an analysis that allows the finite element approximation space to include non-smooth functions and...

Numerical integration for high order pyramidal finite elements

Nilima Nigam, Joel Phillips (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

Similarity:

We examine the effect of numerical integration on the accuracy of high order conforming pyramidal finite element methods. Non-smooth shape functions are indispensable to the construction of pyramidal elements, and this means the conventional treatment of numerical integration, which requires that the finite element approximation space is piecewise polynomial, cannot be applied. We develop an analysis that allows the finite element approximation space to include non-smooth functions...