AffiliationUniv Arizona, Dept Math
MetadataShow full item record
PublisherSpringer Science and Business Media LLC
CitationGillette, A., Hu, K., & Zhang, S. (2019). Nonstandard finite element de Rham complexes on cubical meshes. BIT Numerical Mathematics, 1-37.
JournalBIT Numerical Mathematics
RightsCopyright © Springer Nature B.V. 2019.
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.
AbstractTwo general operations are proposed on finite element differential complexes on cubical meshes that can be used to construct and analyze sequences of "nonstandard" convergent methods. The first operation, called DoF-transfer, moves edge degrees of freedom to vertices in a way that reduces global degrees of freedom while increasing continuity order at vertices. The second operation, called serendipity, eliminates interior bubble functions and degrees of freedom locally on each element without affecting edge degrees of freedom. These operations can be used independently or in tandem to create nonstandard complexes that incorporate Hermite, Adini and "trimmed-Adini" elements. The resulting elements lead to convergent non-conforming methods for problems requiring stronger regularity and satisfy a discrete Korn inequality. Potential benefits of applying these elements to Stokes, biharmonic and elasticity problems are discussed.
Note12 month embargo; published 11 September 2019
VersionFinal accepted manuscript
SponsorsAG was supported in part by National Science Foundation Award DMS-1522289. KH was supported inpart by the European Research Council under the European Union’s Seventh Framework Programme(FP7/2007-2013) / ERC grant agreement 339643. SZ was supported in part by the National NaturalScience Foundation of China with Grant No. 11471026.