Instance optimality of an AFEM with maximum marking strategy

13 March 2014
Professor Christian Kreuzer
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