On the Threshold Condition for Dörfler Marking

It is an open question if the threshold condition for the Dörfler marking parameter is necessary to obtain optimal algebraic rates of adaptive finite element methods. We present a (non-PDE) example fitting into the common abstract convergence framework (axioms of adaptivity) which allows for converg...

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Bibliographic Details
Published inJournal of computational methods in applied mathematics Vol. 21; no. 3; pp. 557 - 567
Main Authors Diening, Lars, Kreuzer, Christian
Format Journal Article
LanguageEnglish
Published Minsk De Gruyter 01.07.2021
Walter de Gruyter GmbH
Subjects
41A25
65N15
65N50
Adaptive Finite Element Methods
Algebra
Axioms
Convergence
Dörfler Marking
Finite element method
Marking
Mathematical analysis
Optimal Complexity
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Summary:It is an open question if the threshold condition for the Dörfler marking parameter is necessary to obtain optimal algebraic rates of adaptive finite element methods. We present a (non-PDE) example fitting into the common abstract convergence framework (axioms of adaptivity) which allows for convergence with exponential rates. However, for Dörfler marking , the algebraic convergence rate can be made arbitrarily small.
ISSN:1609-4840
1609-9389
DOI:10.1515/cmam-2020-0041