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M. Aurada, D. Praetorius, D. Pavlicek:
"Optimalität adaptiver FEM (Supervisor: M. Aurada, D. Praetorius)";
Bericht für Bachelor thesis; 2011.

We analyze the properties which have to be guaranteed by the
mesh-refinement strategy, so that adaptive FEM can be proven to be
optimal: First, the optimality of the closure step to end up with a
regular triangulation, second, the optimality of the overlay of two
meshes obtained. We restrict to triangular meshes in 2D.

For newest vertex bisection (NVB), we recall the proof of Binev,
Dahmen and DeVore (2004) and the proof of Stevenson (2008) to see
that NVB satisfies both optimality conditions.

For a modified red-green-blue refinement (RGB) proposed by Carstensen
(2006), we proof that the closure is still optimal. However, we
give an appropriate counter example to see that the overlay is not.

http://www.asc.tuwien.ac.at/~dirk/download/thesis/bsc/pavlicek2011.pdf