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Numerical integration for high order pyramidalfinite elements

Published online by Cambridge University Press:  12 October 2011

Nilima Nigam  and
Joel Phillips
Nilima Nigam
Affiliation:
Department of Mathematics, Simon Fraser University, 8888 University Drive, Burnaby, BC V5A 1S6, Canada. nigam@math.sfu.ca
Joel Phillips
Affiliation:
Department of Mathematics, University College London, Main Campus Gower Street Bloombury, WC1E 6BT, London, UK. joel.phillips@ucl.ac.uk
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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.

Keywords

Finite elementsquadraturepyramid
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 46 , Issue 2 , March 2012 , pp. 239 - 263
Copyright
© EDP Sciences, SMAI, 2011

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