Workshop Numerische Analysis singulär gestörter Probleme
(anlässlich des 60. Geburtstages von Martin Stynes)

Workshop singulär gestörter Probleme

Vorträge & Folien

With edge based refinement towards anisotropic adaptive refinement in FEM

Rene Schneider (Institut für Numerik, TU-Dresden)

We propose a new paradigm for adaptive mesh refinement. Instead of considering local mesh diameters and their adaption to solution features, we propose to evaluate the benefit of possible refinements in a direct fashion, and to select the most profitable refinements. We demonstrate that based on this approach a directional refinement of triangular elements can be achieved, allowing arbitrarily high aspect ratios.
However, only with the help of edge swapping and/or node removal (directional un-refinement) near optimal performance can be achieved for strongly anisotropic solution features. With these ingredients even re-alignment of the mesh with arbitrary error directions is achieved. Numerical experiments demonstrate the utility of the proposed anisotropic refinement strategy.
Stand: 21. November 2011