<div class="csl-bib-body">
<div class="csl-entry">Lederer, P. L. (2019). <i>A Mass conserving mixed stress formulation for incompressible flows</i> [Dissertation, Technische Universität Wien]. reposiTUm. https://doi.org/10.34726/hss.2019.62042</div>
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dc.identifier.uri
https://doi.org/10.34726/hss.2019.62042
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/5335
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dc.description.abstract
This work deals with the introduction and the analysis of a new finite element method for the discretization of incompressible flows. The main focus essentially lies on the discussion of the linear incompressible Stokes equations. These equations describe the physical behaviour and the relation -- derived from the fundamental Newtonian laws -- between the fluid velocity and the pressure (-gradient). Where the standard variational formulation of the Stokes equations demand a Sobolev regularity of order one for the velocity, we give an answer to the question if it is possible to define a variational formulation demanding a weaker regularity property of the velocity. With respect to a formally equivalent representation of the Stokes equations, we answer this question by the introduction of a new function space used for the definition of the gradient of the velocity. The resulting variational formulation is well-posed if we assume that the divergence of the velocity is square integrable. Thereby, with respect to the standard formulation, where all partial derivatives have to be square integrable, this is a reduced regularity property. We present certain properties of the new defined function space and discuss a proper continuous trace operator and the density of smooth functions. Motivated by this new variational formulation, we present and analyze a new finite element method in the rest of this work. For the approximation of the velocity we can now choose a conforming discrete space. This results in a (physically correct) incompressibility of the velocity field, thus exact mass conservation is provided. For the approximation of the gradient of the velocity we define new matrix-valued finite element shape functions, which are normal-tangential continuous across element interfaces. We present a detailed stability analysis and prove optimal convergence order of the discretization error.
en
dc.language
English
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dc.language.iso
en
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dc.rights.uri
http://rightsstatements.org/vocab/InC/1.0/
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dc.subject
Navier Stokes
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dc.subject
inf-sup condition
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dc.subject
divergence-free
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dc.subject
mixed finite elements
en
dc.subject
weakly symmetric
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dc.title
A Mass conserving mixed stress formulation for incompressible flows
en
dc.type
Thesis
en
dc.type
Hochschulschrift
de
dc.rights.license
In Copyright
en
dc.rights.license
Urheberrechtsschutz
de
dc.identifier.doi
10.34726/hss.2019.62042
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dc.contributor.affiliation
TU Wien, Österreich
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dc.rights.holder
Philip Lukas Lederer
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dc.publisher.place
Wien
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tuw.version
vor
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tuw.thesisinformation
Technische Universität Wien
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tuw.publication.orgunit
E101 - Institut für Analysis und Scientific Computing
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dc.type.qualificationlevel
Doctoral
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dc.identifier.libraryid
AC15327919
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dc.description.numberOfPages
142
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dc.identifier.urn
urn:nbn:at:at-ubtuw:1-122519
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dc.thesistype
Dissertation
de
dc.thesistype
Dissertation
en
tuw.author.orcid
0000-0003-1875-7442
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dc.rights.identifier
In Copyright
en
dc.rights.identifier
Urheberrechtsschutz
de
tuw.advisor.staffStatus
staff
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item.languageiso639-1
en
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item.fulltext
with Fulltext
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item.openaccessfulltext
Open Access
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item.mimetype
application/pdf
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item.openairetype
doctoral thesis
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item.grantfulltext
open
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item.openairecristype
http://purl.org/coar/resource_type/c_db06
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item.cerifentitytype
Publications
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crisitem.author.dept
E101-03-1 - Forschungsgruppe Computational Mathematics in Engineering
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crisitem.author.parentorg
E101-03 - Forschungsbereich Scientific Computing and Modelling