Instance optimality of an AFEM with maximum marking strategy

13 March 2014
14:00
Professor Christian Kreuzer
Abstract
Adaptive finite element methods (AFEMs) with Dörflers marking strategy are known to converge with optimal asymptotical rates. Practical experiences show that AFEMs with a maximum marking strategy produces optimal results thereby being less sensitive to choices of the marking parameter. \\ \\ In this talk, we prove that an AFEM with a modified maximum strategy is even instance optimal for the total error, i.e., for the sum of the error and the oscillation. This is a non-asymptotical optimality result. Our approach uses new techniques based on the minimisation of the Dirichlet energy and a newly developed tree structure of the nodes of admissible triangulations.
  • Computational Mathematics and Applications Seminar