Ruhr University Bochum

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.