C.-M. Pfeiler, D. Praetorius:

"Dörfler marking with minimal cardinality is a linear complexity problem";

Mathematics of Computation,89(2020), 2735 - 2752.

Most adaptive finite element strategies employ the Dörfler marking strategy to single out certain elements of a triangulation T for refinement. In the literature, different algorithms have been proposed to construct the set M of marked elements, 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.

Dörfler marking criterion, adaptive finite element method, optimal complexity

http://dx.doi.org/10.1090/mcom/3553

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