New degrees of freedom for differential forms on cubical meshes
Abstract
We consider new degrees of freedom for higher order differential forms on cubical meshes. The approach is inspired by the idea of Rapetti and Bossavit to define higher order Whitney forms and their degrees of freedom using small simplices. We show that higher order differential forms on cubical meshes can be defined analogously using small cubes and prove that these small cubes yield unisolvent degrees of freedom. Importantly, this approach is compatible with discrete exterior calculus and expands the framework to cover higher order methods on cubical meshes, complementing the earlier strategy based on simplices.
Main Author
Format
Articles
Research article
Published
2023
Series
Subjects
Publication in research information system
Publisher
Springer
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202306163924Käytä tätä linkitykseen.
Review status
Peer reviewed
ISSN
1019-7168
DOI
https://doi.org/10.1007/s10444-023-10047-x
Language
English
Published in
Advances in Computational Mathematics
Citation
- Lohi, J. (2023). New degrees of freedom for differential forms on cubical meshes. Advances in Computational Mathematics, 49(3), Article 42. https://doi.org/10.1007/s10444-023-10047-x
License
Additional information about funding
Open Access funding provided by University of Jyväskylä (JYU).
Copyright© The Author(s) 2023