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dc.contributor.author
Andreev, Roman
dc.date.accessioned
2022-09-12T08:01:44Z
dc.date.available
2017-06-10T11:37:52Z
dc.date.available
2022-09-12T08:01:44Z
dc.date.issued
2013-01
dc.identifier.issn
0272-4979
dc.identifier.issn
1464-3642
dc.identifier.other
10.1093/imanum/drs014
en_US
dc.identifier.uri
http://hdl.handle.net/20.500.11850/59271
dc.description.abstract
The abstract linear parabolic evolution equation is formulated as a well-posed linear operator equation for which a conforming minimal residual Petrov–Galerkin discretization framework is developed: the approximate solution is defined as the minimizer of a suitable functional residual over the discrete test space, and may be obtained numerically from an equivalent algebraic residual minimization problem. This approximate solution is shown to be well defined and to converge quasi-optimally in the natural norm if the discrete trial and test spaces are stable, i.e., if the discrete inf–sup condition is satisfied with a uniform positive lower bound. For the parabolic operator we devise an abstract criterion for the stability of pairs of space–time trial and test spaces, and construct hierarchic families of trial and test spaces of a sparse space–time tensor-product type that satisfy this criterion. The theory is applied to the concrete example of the diffusion equation and is illustrated numerically.
en_US
dc.language.iso
en
en_US
dc.publisher
Oxford University Press
en_US
dc.subject
Minimal residual Petrov–Galerkin
en_US
dc.subject
Space–time discretization
en_US
dc.subject
Parabolic evolution equations
en_US
dc.subject
Sparse tensor product
en_US
dc.title
Stability of sparse space–time finite element discretizations of linear parabolic evolution equations
en_US
dc.type
Journal Article
dc.date.published
2012-06-20
ethz.journal.title
IMA Journal of Numerical Analysis
ethz.journal.volume
33
en_US
ethz.journal.issue
1
en_US
ethz.journal.abbreviated
IMA J. Numer. Anal.
ethz.pages.start
242
en_US
ethz.pages.end
260
en_US
ethz.identifier.wos
ethz.identifier.scopus
ethz.publication.place
Oxford
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::03435 - Schwab, Christoph / Schwab, Christoph
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::03435 - Schwab, Christoph / Schwab, Christoph
ethz.relation.isNewVersionOf
10.3929/ethz-a-010399592
ethz.date.deposited
2017-06-10T11:38:20Z
ethz.source
ECIT
ethz.identifier.importid
imp5936500cd0c8876636
ethz.ecitpid
pub:94797
ethz.eth
yes
en_US
ethz.availability
Metadata only
en_US
ethz.rosetta.installDate
2017-07-26T14:29:09Z
ethz.rosetta.lastUpdated
2018-10-01T18:59:58Z
ethz.rosetta.exportRequired
true
ethz.rosetta.versionExported
true
ethz.COinS
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