Orthogonal polynomials on the semicircle
Walter Gautschi (1990)
Banach Center Publications
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Walter Gautschi (1990)
Banach Center Publications
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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.
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...
Nilima Nigam, Joel Phillips (2011)
ESAIM: Mathematical Modelling and Numerical Analysis
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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...
G. V. Milovanović (2008)
Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques
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Kovačević, M.A., Milovanović, G.V. (1996)
Portugaliae Mathematica
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Sanikidze, J. (2001)
Computational Methods in Applied Mathematics
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