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dc.contributor.author
Hiptmair, Ralf
dc.contributor.author
Pechstein, Clemens
dc.date.accessioned
2021-03-02T06:27:21Z
dc.date.available
2020-12-22T16:02:51Z
dc.date.available
2020-12-23T13:29:23Z
dc.date.available
2021-03-02T06:27:21Z
dc.date.issued
2020
dc.identifier.isbn
978-3-030-39646-6
en_US
dc.identifier.isbn
978-3-030-39647-3
en_US
dc.identifier.issn
1439-7358
dc.identifier.other
10.1007/978-3-030-39647-3_3
en_US
dc.identifier.uri
http://hdl.handle.net/20.500.11850/458213
dc.identifier.doi
10.3929/ethz-b-000458213
dc.description.abstract
We elaborate so-called regular decompositions of vector fields on a three-dimensional Lipschitz domain where the field and its rotation/divergence belong to L2 and where the tangential/normal component of the field vanishes on a sufficiently smooth “Dirichlet” part of the boundary. We impose no restrictions on the topology of the domain, its boundary, or the Dirichlet boundary parts. The field is split into a regular vector field, whose Cartesian components lie in H1 and vanish on the Dirichlet boundary, and a remainder contained in the kernel of the rotation/divergence operator. The decomposition is proved to be stable not only in the natural norms, but also with respect to the L2 norm. Besides, for special cases of mixed boundary conditions, we show the existence of H1-regular potentials that characterize the range of the rotation and divergence operator. We conclude with results on discrete counterparts of regular decompositions for spaces of low-order discrete differential forms on simplicial meshes. Essentially, all results for function spaces carry over, though local correction terms may be necessary. These discrete regular decompositions have become an important tool in finite element exterior calculus (FEEC) and for the construction of preconditioners.
en_US
dc.format
application/pdf
en_US
dc.language.iso
en
en_US
dc.publisher
Springer
en_US
dc.rights.uri
http://creativecommons.org/licenses/by/4.0/
dc.title
A Review of Regular Decompositions of Vector Fields: Continuous, Discrete, and Structure-Preserving
en_US
dc.type
Conference Paper
dc.rights.license
Creative Commons Attribution 4.0 International
dc.date.published
2020-08-12
ethz.book.title
Spectral and High Order Methods for Partial Differential Euqations, ICOSAHOM 2018
en_US
ethz.journal.title
Lecture Notes in Computational Science and Engineering
ethz.journal.volume
134
en_US
ethz.journal.abbreviated
Lect. notes comput. sci. eng.
ethz.pages.start
45
en_US
ethz.pages.end
60
en_US
ethz.version.deposit
publishedVersion
en_US
ethz.event
12th International Conference on Spectral and High-Order Methods (ICOSAHOM 2018)
en_US
ethz.event.location
London, UK
en_US
ethz.event.date
July 9-13, 2018
en_US
ethz.publication.place
Cham
en_US
ethz.publication.status
published
en_US
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics::03632 - Hiptmair, Ralf / Hiptmair, Ralf
en_US
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics::03632 - Hiptmair, Ralf / Hiptmair, Ralf
en_US
ethz.relation.isPartOf
10.3929/ethz-b-000458210
ethz.date.deposited
2020-12-22T16:02:59Z
ethz.source
FORM
ethz.eth
yes
en_US
ethz.availability
Open access
en_US
ethz.rosetta.installDate
2020-12-23T13:29:45Z
ethz.rosetta.lastUpdated
2021-02-15T22:50:00Z
ethz.rosetta.exportRequired
true
ethz.rosetta.versionExported
true
ethz.COinS
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