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Workshop Numerical Analysis for Singularly Perturbed Problems
(dedicated to the 60th birthday of Martin Stynes)

Workshop Singularly Perturbed Problems

Talks & Slides

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.
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Last change: 21 November 2011