Numerical integration for high order pyramidal finite elements

Nilima Nigam; Joel Phillips

ESAIM: Mathematical Modelling and Numerical Analysis (2011)

  • Volume: 46, Issue: 2, page 239-263
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Nigam, Nilima, and Phillips, Joel. "Numerical integration for high order pyramidal finite elements." ESAIM: Mathematical Modelling and Numerical Analysis 46.2 (2011): 239-263. <http://eudml.org/doc/222139>.

@article{Nigam2011,
abstract = { 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. },
author = {Nigam, Nilima, Phillips, Joel},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Finite elements; quadrature; pyramid; higher-order conforming pyramidal finite element methods; quadrature rule; convergence; consistency; discrete de Rham complex},
language = {eng},
month = {10},
number = {2},
pages = {239-263},
publisher = {EDP Sciences},
title = {Numerical integration for high order pyramidal finite elements},
url = {http://eudml.org/doc/222139},
volume = {46},
year = {2011},
}

TY - JOUR
AU - Nigam, Nilima
AU - Phillips, Joel
TI - Numerical integration for high order pyramidal finite elements
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2011/10//
PB - EDP Sciences
VL - 46
IS - 2
SP - 239
EP - 263
AB - 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.
LA - eng
KW - Finite elements; quadrature; pyramid; higher-order conforming pyramidal finite element methods; quadrature rule; convergence; consistency; discrete de Rham complex
UR - http://eudml.org/doc/222139
ER -

References

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