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dc.contributor.author
Dahmen, Wolfgang
dc.contributor.author
Huang, Chunyan
dc.contributor.author
Schwab, Christoph
dc.contributor.author
Welper, Gerrit
dc.date.accessioned
2018-09-19T06:31:11Z
dc.date.available
2018-09-19T06:17:03Z
dc.date.available
2018-09-19T06:31:11Z
dc.date.issued
2011-02
dc.identifier.uri
http://hdl.handle.net/20.500.11850/290329
dc.identifier.doi
10.3929/ethz-a-010401913
dc.description.abstract
We propose a general framework for well posed variational formulations of linear unsymmetric operators, taking first order transport \cs{and evolution} equations in bounded domains as primary orientation. We outline a general variational framework for stable discretizations of boundary value problems for these operators. To adaptively resolve anisotropic solution features such as propagating singularities the variational formulations should allow one, in particular, to employ as trial spaces directional representation systems. Since such systems are known to be stable in $L_2$ special emphasis is placed on $L_2$-stable formulations. The proposed stability concept is based on perturbations of certain "ideal" test spaces in Petrov-Galerkin formulations. We develop a general strategy for realizing corresponding schemes without actually computing excessively expensive test basis functions. Moreover, we develop adaptive solution concepts with provable error reduction. The results are illustrated by first numerical experiments.
en_US
dc.format
application/pdf
en_US
dc.language.iso
en
en_US
dc.publisher
ETH Zürich, Seminar für Angewandte Mathematik
en_US
dc.rights.uri
http://rightsstatements.org/page/InC-NC/1.0/
dc.subject
Linear transport problems
en_US
dc.subject
L2-stable Petrov-Galerkin formulations
en_US
dc.subject
Trace theorems
en_US
dc.subject
δ-proximality
en_US
dc.subject
Adaptive refinement schemes
en_US
dc.subject
Rresidual approximation
en_US
dc.subject
Error reduction
en_US
dc.title
Adaptive Petrov-Galerkin methods for first order transport equations
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dc.type
Report
dc.rights.license
In Copyright - Non-Commercial Use Permitted
ethz.journal.title
Research Report / Seminar für Angewandte Mathematik
ethz.journal.volume
2011-08
en_US
ethz.size
29 p.
en_US
ethz.code.ddc
DDC - DDC::5 - Science::510 - Mathematics
en_US
ethz.publication.place
Zürich
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
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
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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.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
en_US
ethz.relation.isOriginalFormOf
20.500.11850/57678
ethz.date.deposited
2017-06-09T16:48:46Z
ethz.source
ECIT
ethz.source
ECOL
ethz.identifier.importid
imp59364e8f3afd628055
ethz.identifier.importid
imp59366b726f91729783
ethz.ecolpid
eth:47516
ethz.ecitpid
pub:67175
ethz.eth
yes
en_US
ethz.availability
Open access
en_US
ethz.rosetta.installDate
2018-09-19T06:17:11Z
ethz.rosetta.lastUpdated
2018-11-08T02:30:41Z
ethz.rosetta.versionExported
true
dc.identifier.olduri
http://hdl.handle.net/20.500.11850/40057
dc.identifier.olduri
http://hdl.handle.net/20.500.11850/155002
ethz.COinS
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