On the threshold condition for Dörfler marking
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Date
2020-03
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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.
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adaptive finite element methods, Dörfler marking, convergence, optimal complexity