Dörfler marking with minimal cardinality is a linear complexity problem

2019/07/31 by Carl-Martin Pfeiler, Dirk Praetorius · 1 citation
Mathematics · Computer Science · #math.NA #cs.NA #msc:65N50 #msc:65N30 #msc:68Q25

paper · pdf · doi:10.1090/mcom/3553

published as Mathematics of Computation, 89 (2020), 2735-2752 · 20 pages, 1 figure

arxiv created 2020/02/25 · arxiv updated 2020/09/07

Abstract

Most adaptive finite element strategies employ the Dörfler marking strategy to single out certain elements M ⊆ T of a triangulation T for refinement. In the literature, different algorithms have been proposed to construct M, where usually two goals compete: On the one hand, M should contain a minimal number of elements. On the other hand, one aims for linear costs with respect to the cardinality of T. Unlike expected in the literature, we formulate and analyze an algorithm, which constructs a minimal set M at linear costs. Throughout, pseudocodes are given.

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