Numerical integration for high order pyramidal finite elements
Nigam, Nilima ; Phillips, Joel
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 46 (2012), p. 239-263 / Harvested from Numdam
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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 show that, despite this complication, conventional rules of thumb can still be used to select appropriate quadrature methods on pyramids. Along the way, we present a new family of high order pyramidal finite elements for each of the spaces of the de Rham complex.

Publié le : 2012-01-01
DOI : https://doi.org/10.1051/m2an/2011042
Classification:  65N30,  65D30 
@article{M2AN_2012__46_2_239_0,
     author = {Nigam, Nilima and Phillips, Joel},
     title = {Numerical integration for high order pyramidal finite elements},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {46},
     year = {2012},
     pages = {239-263},
     doi = {10.1051/m2an/2011042},
     mrnumber = {2855642},
     zbl = {1276.65083},
     language = {en},
     url = {http://dml.mathdoc.fr/item/M2AN_2012__46_2_239_0}
}

Nigam, Nilima; Phillips, Joel. Numerical integration for high order pyramidal finite elements. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 46 (2012) pp. 239-263. doi : 10.1051/m2an/2011042. http://gdmltest.u-ga.fr/item/M2AN_2012__46_2_239_0/

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