<div class="csl-bib-body">
<div class="csl-entry">Streitberger, J., Brunner, M., Heid, P., Innerberger, M., Miraci, A., & Praetorius, D. (2023, April 27). <i>Adaptive FEM for linear elliptic PDEs: optimal complexity</i> [Conference Presentation]. Austrian Numerical Analysis Day 2023, Wien, Austria.</div>
</div>
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/187373
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dc.description.abstract
We consider a general nonsymmetric second-order linear elliptic PDE in the framework of the Lax–Milgram lemma. We formulate and analyze an adaptive finite element algorithm with arbitrary polynomial degree p that steers the adaptive mesh-refinement and the inexact iterative solution of the arising linear systems. More precisely, the iterative solver employs, as an outer loop, the so-called Zarantonello iteration to symmetrize the system and, as an inner loop, a uniformly contraction algebraic solver, e.g., an optimally preconditioned conjugate gradient method [1] or an optimal geometric multigrid algorithm[2, 3]. We prove that the proposed inexact adaptive iteratively symmetrized finite element method (AISFEM) leads to full linear convergence and, for sufficiently small adaptivity parameters, to optimal convergence rates with respect to the overall computational cost, i.e., the total computational time [4].
en
dc.language.iso
en
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dc.subject
cost-optimality
en
dc.subject
nonsymmetric PDEs
en
dc.subject
adaptive finite element method
en
dc.title
Adaptive FEM for linear elliptic PDEs: optimal complexity
en
dc.type
Presentation
en
dc.type
Vortrag
de
dc.type.category
Conference Presentation
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tuw.researchTopic.id
A3
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tuw.researchTopic.name
Fundamental Mathematics Research
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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.publication.orgunit
E101-02 - Forschungsbereich Numerik
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tuw.publication.orgunit
E101 - Institut für Analysis und Scientific Computing
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tuw.author.orcid
0000-0003-1189-0611
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tuw.author.orcid
0000-0002-1977-9830
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tuw.event.name
Austrian Numerical Analysis Day 2023
en
tuw.event.startdate
27-04-2023
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tuw.event.enddate
28-04-2023
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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
Wien
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tuw.event.country
AT
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tuw.event.institution
Universität Wien
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tuw.event.presenter
Streitberger, Julian
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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 paper not in proceedings
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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/c_18cp
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crisitem.author.dept
E101-02-2 - Forschungsgruppe Numerik von PDEs
-
crisitem.author.dept
E101-02-2 - Forschungsgruppe Numerik von PDEs
-
crisitem.author.dept
Technical University of Munich
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crisitem.author.dept
E101-02-2 - Forschungsgruppe Numerik von PDEs
-
crisitem.author.dept
E101-02-2 - Forschungsgruppe Numerik von PDEs
-
crisitem.author.dept
E101 - Institut für Analysis und Scientific Computing
