Whitney forms and their extensions
Year of publication
2021
Authors
Lohi, Jonni; Kettunen, Lauri
Abstract
Whitney forms are widely known as finite elements for differential forms. Whitney’s original definition yields first order functions on simplicial complexes, and a lot of research has been devoted to extending the definition to nonsimplicial cells and higher order functions. As a result, the term Whitney forms has become somewhat ambiguous in the literature. Our aim here is to clarify the concept of Whitney forms and explicitly explain their key properties. We discuss Whitney’s initial definition with more depth than usually, giving three equivalent ways to define Whitney forms. We give a comprehensive exposition of their main properties, including the proofs. Understanding of these properties is important as they can be taken as a guideline on how to extend Whitney forms to nonsimplicial cells or higher order functions. We discuss several generalisations of Whitney forms and check which of the properties can be preserved.
Show moreOrganizations and authors
Publication type
Publication format
Article
Parent publication type
Journal
Article type
Original article
Audience
ScientificPeer-reviewed
Peer-ReviewedMINEDU's publication type classification code
A1 Journal article (refereed), original researchPublication channel information
Publisher
Volume
393
Article number
113520
ISSN
Publication forum
Publication forum level
2
Open access
Open access in the publisher’s service
Yes
Open access of publication channel
Partially open publication channel
Self-archived
Yes
Other information
Fields of science
Mathematics
Keywords
[object Object],[object Object],[object Object]
Publication country
Netherlands
Internationality of the publisher
International
Language
English
International co-publication
No
Co-publication with a company
No
DOI
10.1016/j.cam.2021.113520
The publication is included in the Ministry of Education and Culture’s Publication data collection
Yes