Affiliation
Univ Arizona, Dept MathIssue Date
2019-03Keywords
Finite element differential formsfinite element exterior calculus
serendipity elements
cubical meshes
cubes
Metadata
Show full item recordPublisher
AMER MATHEMATICAL SOCCitation
Gillette, A., & Kloefkorn, T. (2019). Trimmed serendipity finite element differential forms. Mathematics of Computation, 88(316), 583-606.Journal
MATHEMATICS OF COMPUTATIONRights
Copyright © 2018 American Mathematical Society.Collection Information
This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu.Abstract
We introduce the family of trimmed serendipity finite element differential form spaces, defined on cubical meshes in any number of dimensions, for any polynomial degree, and for any form order. The relation between the trimmed serendipity family and the (non-trimmed) serendipity family developed by Arnold and Awanou [Math. Comp. 83 (2014), pp. 1551-1570] is analogous to the relation between the trimmed and (non-trimmed) polynomial finite element differential form families on simplicial meshes from finite element exterior calculus. We provide degrees of freedom in the general setting and prove that they are unisolvent for the trimmed serendipity spaces. The sequence of trimmed serendipity spaces with a fixed polynomial order r provides an explicit example of a system described by Christiansen and Gillette [ESAIM: M2AN 50 (2016), pp. 883-850], namely, a minimal compatible finite element system on squares or cubes containing order r - 1 polynomial differential forms.ISSN
0025-57181088-6842
Version
Final accepted manuscriptSponsors
NSF [DMS-1522289]Additional Links
https://www.ams.org/mcom/2019-88-316/ae974a485f413a2113503eed53cd6c53
10.1090/mcom/2019-88-316