AffiliationUniv Arizona, Dept Math
KeywordsFinite element differential forms
finite element exterior calculus
MetadataShow full item record
PublisherAMER MATHEMATICAL SOC
CitationGillette, A., & Kloefkorn, T. (2019). Trimmed serendipity finite element differential forms. Mathematics of Computation, 88(316), 583-606.
JournalMATHEMATICS OF COMPUTATION
RightsCopyright © 2018 American Mathematical Society
Collection InformationThis 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 firstname.lastname@example.org.
AbstractWe 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.
VersionFinal accepted manuscript