<div class="csl-bib-body">
<div class="csl-entry">Praetorius, D., Brunner, M., Heid, P., Innerberger, M., Miraci, A., & Streitberger, J. (2023, June 13). <i>Adaptive FEM for linear elliptic PDEs: Optimal complexity</i> [Conference Presentation]. FoCM 2023, Paris, France. http://hdl.handle.net/20.500.12708/191857</div>
</div>
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/191857
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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 AFEM algorithm 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 contractive algebraic solver, e.g., an optimally preconditioned conjugate gradient method or an optimal geometric multigrid algorithm. We show 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.
The talk is based on our recent preprints “Adaptive FEM with quasi-optimal overall cost for nonsymmetric linear elliptic PDEs” (arXiv:2212.00353) and “hp-robust multigrid solver on locally refined meshes for FEM discretizations of symmetric elliptic PDEs” (arXiv:2210.10415).
Joint work with Maximilian Brunner (TU Wien, Austria), Pascal Heid (TU München, Germany), Michael Innerberger (HHMI Janelia Research Campus, USA), Ani Miraci (TU Wien, Austria) and Julian Streitberger (TU Wien, Austria).
en
dc.language.iso
en
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dc.subject
adaptive finite element method
en
dc.subject
semilinear PDE
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dc.subject
optimal cost
en
dc.title
Adaptive FEM for linear elliptic PDEs: Optimal complexity
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dc.type
Presentation
en
dc.type
Vortrag
de
dc.contributor.affiliation
Technical University of Munich, Germany
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dc.type.category
Conference 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.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
FoCM 2023
en
tuw.event.startdate
12-06-2023
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tuw.event.enddate
21-06-2023
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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
Paris
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tuw.event.country
FR
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tuw.event.institution
Sorbonne Université
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tuw.event.presenter
Praetorius, Dirk
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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 paper not in proceedings
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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/c_18cp
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crisitem.author.dept
E101 - Institut für Analysis und Scientific Computing
