[Zurück]

M. Feischl, M. Page, D. Praetorius:
"Convergence and quasi-optimality of adaptive FEM with inhomogeneous Dirichlet data";
Journal of Computational and Applied Mathematics, 255 (2014), S. 481 - 501.

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://dx.doi.org/10.1016/j.cam.2013.06.009