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On the Threshold Condition for Dörfler Marking

  • Lars Diening ORCID logo EMAIL logo and Christian Kreuzer ORCID logo

Abstract

It is an open question if the threshold condition θ < θ 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 θ > θ , the algebraic convergence rate can be made arbitrarily small.

MSC 2010: 65N50; 65N15; 41A25

Award Identifier / Grant number: CRC 1283

Funding statement: The research of Lars Diening was partially supported by the DFG through the CRC 1283.

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Received: 2020-03-24
Revised: 2020-09-22
Accepted: 2020-09-29
Published Online: 2020-10-09
Published in Print: 2021-07-01

© 2020 Walter de Gruyter GmbH, Berlin/Boston

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