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C. Erath, G. Gantner, D. Praetorius:
"Optimal convergence behavior of adaptive FEM driven by simple (h-h/2)-type error estimators";
in: "ASC Report 10/2018", herausgegeben von: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2018, ISBN: 978-3-902627-11-7, S. 1 - 26.

For some Poisson-type model problem, we prove that adaptive FEM driven by the (h − h/2)-type error estimators from [Ferraz-Leite, Ortner, Praetorius, Numer. Math. 116 (2010)] leads to convergence with optimal algebraic convergence rates. Besides the implementational simplicity, another striking feature of these estimators is that they can provide guaranteed lower bounds for the energy error with known efficiency constant 1.

finite element method, a posteriori error estimators, adaptive algorithm, local mesh-refinement, optimal convergence rates.

http://www.asc.tuwien.ac.at/preprint/2018/asc10x2018.pdf