Numerical integration for high order pyramidal finite elements
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 46 (2012) no. 2, p. 239-263

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.

DOI : https://doi.org/10.1051/m2an/2011042
Classification:  65N30,  65D30
Keywords: finite elements, quadrature, pyramid
@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},
     publisher = {EDP-Sciences},
     volume = {46},
     number = {2},
     year = {2012},
     pages = {239-263},
     doi = {10.1051/m2an/2011042},
     zbl = {1276.65083},
     mrnumber = {2855642},
     language = {en},
     url = {http://www.numdam.org/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, Volume 46 (2012) no. 2, pp. 239-263. doi : 10.1051/m2an/2011042. http://www.numdam.org/item/M2AN_2012__46_2_239_0/

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