<div class="csl-bib-body">
<div class="csl-entry">Becker, R., Gantner, G., Innerberger, M., & Praetorius, D. (2023). Goal-oriented adaptive finite element methods with optimal computational complexity. <i>Numerische Mathematik</i>, <i>153</i>, 111–140. https://doi.org/10.1007/s00211-022-01334-8</div>
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dc.identifier.issn
0029-599X
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/191012
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dc.description.abstract
We consider a linear symmetric and elliptic PDE and a linear goal functional. We design and analyze a goal-oriented adaptive finite element method, which steers the adaptive mesh-refinement as well as the approximate solution of the arising linear systems by means of a contractive iterative solver like the optimally preconditioned conjugate gradient method or geometric multigrid. We prove linear convergence of the proposed adaptive algorithm with optimal algebraic rates. Unlike prior work, we do not only consider rates with respect to the number of degrees of freedom but even prove optimal complexity, i.e., optimal convergence rates with respect to the total computational cost.
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dc.description.sponsorship
FWF - Österr. Wissenschaftsfonds
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dc.description.sponsorship
FWF - Österr. Wissenschaftsfonds
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dc.language.iso
en
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dc.publisher
SPRINGER HEIDELBERG
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dc.relation.ispartof
Numerische Mathematik
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dc.rights.uri
http://creativecommons.org/licenses/by/4.0/
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dc.subject
Optimal Computational Cost
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dc.subject
Optimal Convergence Rates
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dc.subject
Convergence of Adaptive FEM
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dc.subject
Finite Element Method
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dc.subject
Goal-Oriented Algorithm
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dc.subject
Adaptivity
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dc.title
Goal-oriented adaptive finite element methods with optimal computational complexity