TY - GEN A1 - Gallistl, Dietmar T1 - An Optimal Adaptive FEM for Eigenvalue Clusters N2 - The analysis of adaptive finite element methods in practice immediately leads to eigenvalue clusters which requires the simultaneous marking in adaptive finite element methods. A first analysis for multiple eigenvalues of the recent work [Dai, He, Zhou, arXiv Preprint 1210.1846v2] introduces an adaptive method whose marking strategy is based on the element-wise sum of local error estimator contributions for multiple eigenvalues. This paper proves optimality of a practical adaptive algorithm for eigenvalue clusters for the eigenvalues of the Laplace operator in terms of nonlinear approximation classes. All estimates are explicit in the initial mesh-size, the eigenvalues and the cluster width to clarify the dependence of the involved constants. KW - eigenvalue problem, eigenvalue cluster, adaptive finite element method, optimality Y1 - 2014 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/1287 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-12870 ER -