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M. Feischl, M. Page, D. Praetorius:
"Convergence and quasi-optimality of adaptive FEM with inhomogeneous Dirichlet data (GAMM 2011)";
in: "ASC Report 16/2011", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2011, ISBN: 978-3-902627-04-9.

We consider an adaptive mesh-refining algorithm for a lowest-order finite element method (AFEM). Contrary to prior works,
where the Poisson equation with homogeneous Dirichlet data is analyzed, our focus is on the case of inhomogeneous Dirichlet
data g 6= 0. As is usually done in practice, we use nodal interpolation to discretize g. Besides convergence of AFEM, which
is proven by means of an appropriate contraction quantity, we also discuss quasi-optimality of the proposed algorithm.

http://www.asc.tuwien.ac.at/preprint/2011/asc16x2011.pdf