Spaces of finite element differential forms

Douglas N. Arnold

Research output: Chapter in Book/Report/Conference proceedingChapter

13 Scopus citations

Abstract

We discuss the construction of finite element spaces of differential forms which satisfy the crucial assumptions of the finite element exterior calculus, namely that they can be assembled into subcomplexes of the de Rham complex which admit commuting projections. We present two families of spaces in the case of simplicial meshes, and two other families in the case of cubical meshes. We make use of the exterior calculus and the Koszul complex to define and understand the spaces. These tools allow us to treat a wide variety of situations, which are often treated separately, in a unified fashion.

Original languageEnglish (US)
Title of host publicationSpringer INdAM Series
PublisherSpringer International Publishing
Pages117-140
Number of pages24
DOIs
StatePublished - 2013

Publication series

NameSpringer INdAM Series
Volume4
ISSN (Print)2281-518X
ISSN (Electronic)2281-5198

Bibliographical note

Funding Information:
The work of the author was supported by NSF grant DMS-1115291.

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