<div class="csl-bib-body">
<div class="csl-entry">Bringmann, P., Feischl, M., Miraci, A., Praetorius, D., & Streitberger, J. (2024, August 8). <i>On full linear convergence and optimal complexity of adaptive FEM with inexact solver</i> [Presentation]. 2CCC Workshop on Numerical Analysis 2024, Berlin, Germany.</div>
</div>
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/199864
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dc.description.abstract
The ultimate goal of any numerical scheme for partial differential equations (PDEs) is to compute an approximation of user-prescribed accuracy at quasi-minimal computational time. To this end, the algorithmic realization of a standard adaptive finite element method (AFEM) integrates an inexact solver and nested iterations with discerning stopping criteria to balance the different error components. The analysis ensuring optimal convergence order of AFEM with respect to the overall computational cost critically hinges on the concept of R-linear convergence of a suitable quasi-error quantity. This talk presents recent advances in the analysis of AFEMs to overcome several shortcomings of previous approaches. First, a new proof strategy with a summability criterion for R-linear convergence allows removing typical restrictions on the stopping parameters of the nested adaptive algorithm. Second, the usual assumption of a (quasi-)Pythagorean identity is replaced by the generalized notion of quasi-orthogonality from [Feischl, Math. Comp., 91 (2022)]. Importantly, this paves the way towards extending the analysis to general inf-sup stable problems beyond the energy minimization setting. Numerical experiments investigate the choice of the adaptivity and stopping parameters.
en
dc.language.iso
en
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dc.subject
adaptive finite element method
en
dc.subject
optimal convergence rates
en
dc.subject
cost-optimality
en
dc.subject
inexact solver
en
dc.subject
full linear convergence
en
dc.title
On full linear convergence and optimal complexity of adaptive FEM with inexact solver
en
dc.type
Presentation
en
dc.type
Vortrag
de
dc.type.category
Presentation
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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
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tuw.publication.orgunit
E101-02-2 - Forschungsgruppe Numerik von PDEs
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tuw.author.orcid
0000-0002-4546-5165
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tuw.author.orcid
0000-0002-1977-9830
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tuw.author.orcid
0000-0003-1189-0611
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tuw.event.name
2CCC Workshop on Numerical Analysis 2024
en
tuw.event.startdate
08-08-2024
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tuw.event.enddate
08-08-2024
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tuw.event.online
On Site
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tuw.event.type
Event for scientific audience
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tuw.event.place
Berlin
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tuw.event.country
DE
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tuw.event.institution
Humboldt-Universität zu Berlin
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tuw.event.presenter
Bringmann, Philipp
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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.languageiso639-1
en
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item.openairetype
conference presentation
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item.grantfulltext
none
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item.fulltext
no Fulltext
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item.cerifentitytype
Publications
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item.openairecristype
http://purl.org/coar/resource_type/R60J-J5BD
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crisitem.author.dept
E101-02-2 - Forschungsgruppe Numerik von PDEs
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crisitem.author.dept
E101-02-3 - Forschungsgruppe Computational PDEs
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crisitem.author.dept
E101-02-2 - Forschungsgruppe Numerik von PDEs
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crisitem.author.dept
E101 - Institut für Analysis und Scientific Computing
