<div class="csl-bib-body">
<div class="csl-entry">Innerberger, M., Miraçi, A., Praetorius, D., & Streitberger, J. (2024). hp-robust multigrid solver on locally refined meshes for FEM discretizations of symmetric elliptic PDEs. <i>ESAIM: Mathematical Modelling and Numerical Analysis</i>, <i>58</i>(1), 247–272. https://doi.org/10.1051/m2an/2023104</div>
</div>
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dc.identifier.issn
2822-7840
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/194185
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dc.description.abstract
In this work, we formulate and analyze a geometric multigrid method for the iterative solution of the discrete systems arising from the finite element discretization of symmetric second-order linear elliptic diffusion problems. We show that the iterative solver contracts the algebraic error robustly with respect to the polynomial degree $p \ge 1$ and the (local) mesh size $h$. We further prove that the built-in algebraic error estimator which comes with the solver is $hp$-robustly equivalent to the algebraic error. The application of the solver within the framework of adaptive finite element methods with quasi-optimal computational cost is outlined. Numerical experiments confirm the theoretical findings.
en
dc.description.sponsorship
FWF - Österr. Wissenschaftsfonds
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dc.description.sponsorship
FWF - Österr. Wissenschaftsfonds
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dc.language.iso
en
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dc.publisher
EDP Sciences
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dc.relation.ispartof
ESAIM: Mathematical Modelling and Numerical Analysis
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dc.rights.uri
http://creativecommons.org/licenses/by/4.0/
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dc.subject
adaptive finite element method
en
dc.subject
local multigrid
en
dc.subject
$hp$-robustness
en
dc.subject
stable decomposition
en
dc.title
hp-robust multigrid solver on locally refined meshes for FEM discretizations of symmetric elliptic PDEs
en
dc.type
Article
en
dc.type
Artikel
de
dc.rights.license
Creative Commons Namensnennung 4.0 International
de
dc.rights.license
Creative Commons Attribution 4.0 International
en
dc.description.startpage
247
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dc.description.endpage
272
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dc.relation.grantno
F 6509-N36
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dc.relation.grantno
P 33216-N
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dc.rights.holder
(c) The authors
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dc.type.category
Original Research Article
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tuw.container.volume
58
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tuw.container.issue
1
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tuw.journal.peerreviewed
true
-
tuw.peerreviewed
true
-
tuw.project.title
Analytische und numerische Koppelung im Mikromagnetismus
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tuw.project.title
Computational nonlinear PDEs
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tuw.researchTopic.id
C4
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tuw.researchTopic.name
Mathematical and Algorithmic Foundations
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tuw.researchTopic.value
100
-
dcterms.isPartOf.title
ESAIM: Mathematical Modelling and Numerical Analysis
-
tuw.publication.orgunit
E101-02-2 - Forschungsgruppe Numerik von PDEs
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tuw.publisher.doi
10.1051/m2an/2023104
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dc.date.onlinefirst
2024-02-16
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dc.identifier.eissn
2804-7214
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dc.identifier.libraryid
AC17202891
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dc.description.numberOfPages
26
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tuw.author.orcid
0000-0002-1977-9830
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tuw.author.orcid
0000-0003-1189-0611
-
dc.rights.identifier
CC BY 4.0
de
dc.rights.identifier
CC BY 4.0
en
wb.sci
true
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wb.sciencebranch
Mathematik
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wb.sciencebranch.oefos
1010
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wb.sciencebranch.value
100
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item.openaccessfulltext
Open Access
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item.cerifentitytype
Publications
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item.languageiso639-1
en
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http://purl.org/coar/resource_type/c_2df8fbb1
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item.grantfulltext
open
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item.fulltext
with Fulltext
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application/pdf
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item.openairetype
research article
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crisitem.author.dept
E101-02-2 - Forschungsgruppe Numerik von PDEs
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crisitem.author.dept
E101-02-2 - Forschungsgruppe Numerik von PDEs
-
crisitem.author.dept
E101 - Institut für Analysis und Scientific Computing