On the threshold condition for Dörfler marking

2020/03/24 by Diening, Lars, Kreuzer, Christian
#41A25 #65N15 #65N50 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2003.10940

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) and which is potentially converging with exponential rates. However, for Dörfler marking θ> θ_⋆ the algebraic converges rate can be made arbitrarily small.

Related

• Axioms of adaptivity for separate marking
• Convergence rates for adaptive finite elements
• Quasi-optimal convergence rate for adaptive mixed finite element methods
• Quasi-optimal convergence rate of an AFEM for quasi-linear problems
• Adaptive boundary element methods with convergence rates