Numerical Integration for High Order Pyramidal Elements

Peer reviewed: 
Yes, item is peer reviewed.
Scholarly level: 
Faculty/Staff
Date created: 
2011
Keywords: 
Finite elements
quadrature
pyramid
Abstract: 

We examine the effect of numerical integration on the accuracy of high order conformingpyramidal finite element methods. Non-smooth shape functions are indispensable to the construction ofpyramidal elements, and this means the conventional treatment of numerical integration, which requiresthat the finite element approximation space is piecewise polynomial, cannot be applied. We developan analysis that allows the finite element approximation space to include non-smooth functions andshow that, despite this complication, conventional rules of thumb can still be used to select appropriatequadrature methods on pyramids. Along the way, we present a new family of high order pyramidalfinite elements for each of the spaces of the de Rham complex.

Language: 
English
Document type: 
Article
Rights holder: 
Copyright ESAIM. The original publication is available at www.esaim-m2an.org
Citation: 
Nilima Nigam and Joel Phillips (2012). Numerical integration for high order pyramidal finite elements. ESAIM: Mathematical Modelling and Numerical Analysis, 46 , pp 239-263 doi:10.1051/m2an/2011042
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