# Meeting Details

Title: Adaptive nonconforming finite element approximation of eigenvalue clusters CCMA PDEs and Numerical Methods Seminar Series Dietmar Gallistl, Humboldt-Universität zu Berlin http://www2.mathematik.hu-berlin.de/~gallistl/index.html/index_english.html This talk presents optimal convergence rates of an adaptive nonconforming FEM for eigenvalue clusters. New techniques from the medius analysis enable the proof of $L^2$ error estimates and best-approximation properties for nonconforming finite element methods and thereby lead to the proof of optimality. Applications include the nonconforming $\mathcal P_1$ FEM for the eigenvalues of the Stokes system and the Morley FEM for the eigenvalues of the biharmonic operator. The optimality in terms of the concept of nonlinear approximation classes is concerned with the approximation of invariant subspaces spanned by eigenfunctions of an eigenvalue cluster. In order to obtain eigenvalue error estimates, this talk presents new estimates for nonconforming finite elements which relate the error of the eigenvalue approximation to the error of the approximation of the invariant subspace.