<div class="csl-bib-body">
<div class="csl-entry">Miraci, A., Brunner, M., Heid, P., Innerberger, M., Praetorius, D., & Streitberger, J. (2023, March 22). <i>Adaptive FEM for linear elliptic PDEs: Optimal complexity</i> [Presentation]. Finite Element Workshop 2023, Jena, Germany. http://hdl.handle.net/20.500.12708/189933</div>
</div>
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/189933
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dc.description.abstract
We consider a general nonsymmetric second-order linear elliptic partial differential equation in the framework of the Lax–Milgram lemma. We formulate and analyze an adaptive finite element algorithm with arbitrary polynomial degree that steers the adaptive meshrefinement 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 contractive algebraic solver, for example, an optimally preconditioned conjugate gradient method or an optimal geometric multigrid algorithm. We prove that the proposed inexact adaptive iteratively symmetrized finite element method 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. Numerical experiments underline the theory.
en
dc.language.iso
en
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dc.subject
adaptive finite element method
en
dc.subject
iterative solver
en
dc.subject
nonsymmetric PDEs
en
dc.subject
optimal convergence rates
en
dc.subject
cost-optimality
en
dc.title
Adaptive FEM for linear elliptic PDEs: Optimal complexity
en
dc.type
Presentation
en
dc.type
Vortrag
de
dc.contributor.affiliation
Technical University of Munich, Germany
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dc.type.category
Presentation
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tuw.publication.invited
invited
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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.publication.orgunit
E129-02 - Fachbereich TUForMath
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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
Finite Element Workshop 2023
en
tuw.event.startdate
20-03-2023
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tuw.event.enddate
22-03-2023
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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
Jena
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tuw.event.country
DE
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tuw.event.presenter
Miraci, Ani
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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.grantfulltext
none
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item.languageiso639-1
en
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item.openairetype
conference presentation
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item.cerifentitytype
Publications
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item.fulltext
no Fulltext
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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
-
crisitem.author.dept
E101-02-2 - Forschungsgruppe Numerik von PDEs
-
crisitem.author.dept
Technical University of Munich
-
crisitem.author.dept
E101-02-2 - Forschungsgruppe Numerik von PDEs
-
crisitem.author.dept
E101 - Institut für Analysis und Scientific Computing
