| Issue |
ESAIM: M2AN
Volume 46, Number 2, November-December 2012
|
|
|---|---|---|
| Page(s) | 239 - 263 | |
| DOI | https://doi.org/10.1051/m2an/2011042 | |
| Published online | 12 October 2011 | |
Numerical integration for high order pyramidal finite elements
1
Department of Mathematics, Simon Fraser University,
8888 University Drive, Burnaby, BC V5A 1S6,
Canada. nigam@math.sfu.ca
2
Department of Mathematics, University College London, Main Campus Gower Street Bloombury, WC1E 6BT, London, UK. joel.phillips@ucl.ac.uk
Received:
23
November
2010
Revised:
16
June
2011
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.
Mathematics Subject Classification: 65N30 / 65D30
Key words: Finite elements / quadrature / pyramid
© EDP Sciences, SMAI, 2011
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