TY - GEN A1 - Carstensen, Carsten A1 - Gedicke, Joscha T1 - An Oscillation-Free Adaptive FEM For Symmetric Eigenvalue Problems N2 - A refined a posteriori error analysis for symmetric eigenvalue problems and the convergence of the first-order adaptive finite element method (AFEM) is presented. The $H^1$ stability of the $L^2$ projection provides reliability and efficiency of the edge-contribution of standard residual-based error estimators for $P_1$ finite element methods. In fact, the volume contributions and even oscillations can be omitted for Courant finite element methods. This allows for a refined averaging scheme and so improves [Dong Mao, Lihua Shen and Aihui Zhou, Adaptive finite element algorithms for eigenvalue problems based on local averaging type a posteriori error estimates, Advanced in Computational Mathematics, 2006, 25: 135-160]. The proposed AFEM monitors the edge-contributions in a bulk criterion and so enables a contraction property up to higher-order terms and global convergence. Numerical experiments exploit the remaining $L^2$ error contributions and confirm our theoretical findings. The averaging schemes show a high accuracy and the AFEM leads to optimal empirical convergence rates. KW - AFEM KW - eigenvalue problems KW - convergence Y1 - 2008 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/491 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-4915 ER -