<div class="csl-bib-body">
<div class="csl-entry">Miraci, A., Innerberger, M., Papež, J., Praetorius, D., Streitberger, J., & Vohralik, M. (2024, May 14). <i>Role of hp-Robust Iterative Solvers in Adaptive Finite Element Algorithms for Optimal Complexity</i> [Conference Presentation]. SIAM Conference on Applied Linear Algebra (LA24), Paris, France. http://hdl.handle.net/20.500.12708/201161</div>
</div>
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/201161
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dc.description.abstract
Adaptive finite element methods (AFEM) have been successfully used in numerical solutions of partial differential equations (PDEs) yielding optimal convergence rates with respect to degrees of freedom. However, due to the nature of AFEM, each refinement step requires a new set of computations leading to cumulated work. One then strives to achieve optimality with respect to overall cost, i.e. total elapsed time. The core question becomes to design contractive algebraic iterative solvers used within AFEM. In the context of symmetric linear elliptic second order PDEs, we propose a local adaptive multigrid solver, where the linear system stems from a finite element discretization with polynomial degree p and bisection-generated meshes with local size h. The proposed solver contracts the algebraic error hp-robustly and comes with a built-in a posteriori error estimator. This estimator provides a two-sided bound of the algebraic error. More precisely, proving the hp-robust contraction of the solver is in fact equivalent to showing that the built-in estimator provides an hp-robust upper bound on the algebraic error. Moreover, the error-equivalent estimator and its localized decomposition leads to the development of an extension of the solver with an adaptive number of additional local smoothing steps assuring further error contraction. Presented numerical results highlight the performance of the solver, its adaptive version, and optimality of the full algorithm.
en
dc.language.iso
en
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dc.subject
adaptive FEM
en
dc.subject
multigrid method
en
dc.subject
hp-robustness
en
dc.subject
optimal rates
en
dc.subject
optimal complexity
en
dc.title
Role of hp-Robust Iterative Solvers in Adaptive Finite Element Algorithms for Optimal Complexity
en
dc.type
Presentation
en
dc.type
Vortrag
de
dc.contributor.affiliation
Czech Academy of Sciences, Institute of Mathematics, Czechia
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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.author.orcid
0009-0003-8335-3302
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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
SIAM Conference on Applied Linear Algebra (LA24)
en
tuw.event.startdate
13-05-2024
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tuw.event.enddate
17-05-2024
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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
Paris
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tuw.event.country
FR
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tuw.event.institution
SIAM
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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.openairecristype
http://purl.org/coar/resource_type/c_18cp
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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.languageiso639-1
en
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item.grantfulltext
none
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crisitem.author.dept
E101-02-2 - Forschungsgruppe Numerik von PDEs
-
crisitem.author.dept
E101-02-2 - Forschungsgruppe Numerik von PDEs
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crisitem.author.dept
Czech Academy of Sciences, Institute of Mathematics
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crisitem.author.dept
E101 - Institut für Analysis und Scientific Computing
