On the threshold condition for Dörfler marking

03/24/2020

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by   Lars Diening, et al.

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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.