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M. Page, D. Praetorius:
"Convergence of adaptive FEM for some elliptic obstacle problem";
Applicable Analysis, 92 (2013), 3; 595 - 615.

In this work, we treat the convergence of adaptive lowest-order FEM
for some elliptic obstacle problem with affine obstacle. For error
estimation, we use a residual error estimator from [Braess,
Carstensen, Hoppe 2007]. We extend recent ideas from [Cascon,
Kreuzer, Nochetto, Siebert 2008] for the unrestricted variational
problem to overcome the lack of Galerkin orthogonality. The main
result states that an appropriately weighted sum of energy error,
edge residuals, and data oscillations satisfies a contraction
property within each step of the adaptive feedback loop. This result
is superior to a prior result from [Braess, Carstensen, Hoppe 2007]
in two ways: First, it is unnecessary to control the decay of the
data oscillations explicitly. Second, our analysis avoids the use of
some discrete local efficiency estimate so that the local
mesh-refinement is fairly arbitrary.

http://dx.doi.org/10.1080/00036811.2011.631916