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

"Convergence and quasi-optimality of adaptive FEM with inhomogeneous Dirichlet data";

in: "ASC Report 34/2010", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2010, ISBN: 978-3-902627-03-2.

We consider the solution of a second order elliptic PDE in 2D with

inhomogeneous Dirichlet data by means of adaptive lowest-order FEM. As

is usually done in practice, the given Dirichlet data are discretized

by nodal interpolation. As model example serves the Poisson equation

with mixed Dirichlet-Neumann boundary conditions. For error estimation,

we use an edge-based residual error estimator which replaces the volume

residual contributions by edge oscillations. We consider two marking

strategies from the literature and prove that either of them is

convergent with quasi-optimal convergence behaviour. Numerical

experiments conclude the work.

http://www.asc.tuwien.ac.at/preprint/2010/asc34x2010.pdf

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