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Numerical Integration for High Order Pyramidal Elements

Resource type
Date created
2011
Authors/Contributors
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.
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Copyright is held by the author(s).
Scholarly level
Peer reviewed?
Yes
Language
English
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