[Back]

M. Page, D. Praetorius:
"Convergence of adaptive FEM for some elliptic obstacle problem";
in: "ASC Report 05/2010", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2010, ISBN: 978-3-902627-03-2.

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 a discrete local efficiency
so that the local mesh-refinement is fairly arbitrary.

http://www.asc.tuwien.ac.at/preprint/2010/asc05x2010.pdf