Talks and Poster Presentations (without Proceedings-Entry):

M. Aurada, M. Feischl, T. Führer, M. Karkulik, M. Page, D. Praetorius:
"What is quasi-optimality of adaptive FEM?";
Keynote Lecture: TCSE Vienna Workshop 2012, Trends in Computational Science and Engineering, Wien (invited); 02-13-2012 - 02-14-2012.

English abstract:
Usually the accuracy of numerical results suffers from singularities
of the given data and/or the (unknown) exact solution. One remedy is
to appropriately grade the underlying mesh towards these singularities. In
many codes, this mesh adaptation is done automatically by use of certain
(heuristic) refinement indicators. Empirically, most of these
adaptive strategies perform very well in the sense that the slope
of number of unknowns versus corresponding error shows the
best possible decay. Such an observation is of practical relevance
since each simulation aims for the best possible solution with respect
to limited resources like computational time and/or memory requirements.
In recent years and for a certain class of elliptic differential equations,
there has been a major breakthrough in the mathematical understanding of
this empirical observation. In our talk, we aim to state "optimal convergence
behaviour" of the numerical scheme in a mathematical sense. We discuss
the progress made in the recent years and highlight some of the mathematical
ingredients for such an optimality proof.

Created from the Publication Database of the Vienna University of Technology.