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.
Mots-clés : 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 }, pages = {239--263}, publisher = {EDP-Sciences}, volume = {46}, number = {2}, year = {2012}, doi = {10.1051/m2an/2011042}, mrnumber = {2855642}, zbl = {1276.65083}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/m2an/2011042/} }
TY - JOUR AU - Nigam, Nilima AU - Phillips, Joel TI - Numerical integration for high order pyramidal finite elements JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2012 SP - 239 EP - 263 VL - 46 IS - 2 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an/2011042/ DO - 10.1051/m2an/2011042 LA - en ID - M2AN_2012__46_2_239_0 ER -
%0 Journal Article %A Nigam, Nilima %A Phillips, Joel %T Numerical integration for high order pyramidal finite elements %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2012 %P 239-263 %V 46 %N 2 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an/2011042/ %R 10.1051/m2an/2011042 %G en %F M2AN_2012__46_2_239_0
Nigam, Nilima; Phillips, Joel. Numerical integration for high order pyramidal finite elements. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 46 (2012) no. 2, pp. 239-263. doi : 10.1051/m2an/2011042. http://archive.numdam.org/articles/10.1051/m2an/2011042/
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