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S. Ferraz-Leite, C. Ortner, D. Praetorius:
"Convergence of simple adaptive Galerkin schemes based on h-h/2 error estimators";
Numerische Mathematik, 116 (2010), ISBN: 978-3-902627-02-5; S. 291 - 316.

We discuss several adaptive mesh-refinement strategies based on $h-h/2$-error
estimation. This class of adaptive methods is particularly popular in
practise since it is problem independent and requires virtually no
implementational overhead. We prove that, under the saturation assumption,
these adaptive algorithms are convergent. Our framework applies not only to
finite element methods, but also yields a first convergence proof for
adaptive boundary element schemes. For a finite element model problem, we
extend the proposed adaptive scheme and prove convergence even if the
saturation assumption fails to hold in general.

http://dx.doi.org/10.1007/s00211-010-0292-9

http://www.springerlink.com/content/r641473j20h1t814/fulltext.pdf