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Common and Unusual Finite Elements

Chapter in book
Authors Robert C. Kirby
Anders Logg
Marie E. Rognes
Andy R. Terrel
Published in Automated Solution of Differential Equations by the Finite Element Method. Anders Logg, Kent-Andre Mardal, Garth Wells (Eds.)
Pages 95-119
ISBN 978-3-642-23098-1
Publisher Springer
Place of publication Heidelberg
Publication year 2012
Published at Department of Mathematical Sciences, Mathematics
Pages 95-119
Language en
Subject categories Mathematics, Computational Mathematics


This chapter provides a glimpse of the considerable range of finite elements in the literature. Many of the elements presented here are implemented as part of the FEniCS project already; some are future work. The universe of finite elements extends far beyond what we consider here. In particular, we consider only simplicial, polynomial-based elements. We thus bypass elements defined on quadrilaterals and hexahedra, composite and macro-element techniques, as well as XFEM-type methods. Even among polynomial-based elements on simplices, the list of elements can be extended. Nonetheless, this chapter presents a comprehensive collection of some the most common, and some more unusual, finite elements.

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