M. Feischl, M. Page, D. Praetorius:

"Convergence of adaptive FEM for some elliptic obstacle problem with inhomogeneous Dirichlet data";

in: "ASC Report 33/2010", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2010, ISBN: 978-3-902627-03-2.

In this work, we show the convergence of adaptive lowest-order FEM

(AFEM) for an elliptic obstacle problem with globally affine obstacle

and non-homogeneous Dirichlet data. The adaptive loop is steered by

some residual based error estimator introduced in Braess, Carstensen

& Hoppe (2007) that is extended to control oscillations of the Dirichlet

data, as well. In the spirit of Cascon et al. (2008), we show that a

weighted sum of energy error, estimator, and Dirichlet oscillations

satisfies a contraction property up to certain vanishing energy

contributions. This result extends the analysis of Braess, Carstensen

& Hoppe (2007) and Page & Praetorius (2009) to the case of

non-homogeneous Dirichlet data and introduces some energy estimates to

overcome the lack of nestedness of the discrete spaces. A short

conclusion adresses AFEM for problems with non-affine obstacles.

http://www.asc.tuwien.ac.at/preprint/2010/asc33x2010.pdf

Created from the Publication Database of the Vienna University of Technology.