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In this work, we show the convergence of adaptive lowest-order FEM (AFEM) foran elliptic obstacle problem with non-homogeneous Dirichlet data, where theobstacle \chi\ is restricted only by \chi\ in H^2(\Omega). The adaptive loop issteered 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 ofenergy error, estimator, and Dirichlet oscillations satisfies a contractionproperty up to certain vanishing energy contributions. This result extends theanalysis of Braess, Carstensen & Hoppe (2007) and Page & Praetorius (2010) tothe case of non-homogeneous Dirichlet data as well as certain non-affineobstacles and introduces some energy estimates to overcome the lack ofnestedness of the discrete spaces.

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