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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Dörfler marking with minimal cardinality is a linear complexity problem
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by Carl-Martin Pfeiler and Dirk Praetorius HTML | PDF
Math. Comp. 89 (2020), 2735-2752 Request permission

Abstract:

Most adaptive finite element strategies employ the Dörfler marking strategy to single out certain elements $\mathcal {M} \subseteq \mathcal {T}$ of a triangulation $\mathcal {T}$ for refinement. In the literature, different algorithms have been proposed to construct $\mathcal {M}$, where usually two goals compete. On the one hand, $\mathcal {M}$ should contain a minimal number of elements. On the other hand, one aims for linear costs with respect to the cardinality of $\mathcal {T}$. Unlike expected in the literature, we formulate and analyze an algorithm, which constructs a minimal set $\mathcal {M}$ at linear costs. Throughout, pseudocodes are given.
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Additional Information
  • Carl-Martin Pfeiler
  • Affiliation: TU Wien, Institute of Analysis and Scientific Computing, Wiedner Hauptstr. 8-10/E101/4, 1040 Vienna, Austria
  • MR Author ID: 1323723
  • Email: carl-martin.pfeiler@asc.tuwien.ac.at
  • Dirk Praetorius
  • Affiliation: TU Wien, Institute of Analysis and Scientific Computing, Wiedner Hauptstr. 8-10/E101/4, 1040 Vienna, Austria
  • MR Author ID: 702616
  • ORCID: 0000-0002-1977-9830
  • Email: dirk.praetorius@asc.tuwien.ac.at
  • Received by editor(s): July 31, 2019
  • Received by editor(s) in revised form: February 25, 2020
  • Published electronically: June 24, 2020
  • Additional Notes: The authors thankfully acknowledge support by the Austrian Science Fund (FWF) through the doctoral school Dissipation and dispersion in nonlinear PDEs (grant W1245) and through the research project Optimal adaptivity for BEM and FEM-BEM coupling (grant P27005).
    The first author is the corresponding author.
  • © Copyright 2020 American Mathematical Society
  • Journal: Math. Comp. 89 (2020), 2735-2752
  • MSC (2010): Primary 65N50, 65N30, 68Q25
  • DOI: https://doi.org/10.1090/mcom/3553
  • MathSciNet review: 4136545