@Article{IJNAM-11-1,
author = {},
title = {Convergence of Adaptive FEM for Some Elliptic Obstacle Problem with Inhomogeneous Dirichlet Data},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2014},
volume = {11},
number = {1},
pages = {229--253},
abstract = {<p style="text-align: justify;">In this work, we show the convergence of adaptive lowest-order FEM (AFEM) for an elliptic obstacle problem with non-homogeneous Dirichlet data, where the obstacle $\chi$ is restricted
only by $\chi\in H^2(\Omega)$. The adaptive loop is steered by some residual based error estimator introduced
in Braess, Carstensen &amp; 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 &amp; Hoppe (2007)
and Page &amp; Praetorius (2013) to the case of non-homogeneous Dirichlet data as well as certain
non-affine obstacles and introduces some energy estimates to overcome the lack of nestedness of
the discrete spaces.</p>},
issn = {2617-8710},
doi = {https://doi.org/2014-IJNAM-523},
url = {https://global-sci.com/article/83336/convergence-of-adaptive-fem-for-some-elliptic-obstacle-problem-with-inhomogeneous-dirichlet-data}
}