TY - GEN A1 - Carstensen, Carsten A1 - Gedicke, Joscha A1 - Mehrmann, Volker A1 - Miedlar, Agnieszka T1 - An Adaptive Finite Element Method with Asymptotic Saturation for Eigenvalue Problems N2 - This paper discusses adaptive finite element methods (AFEMs) for the solution of elliptic eigenvalue problems associated with partial differential operators. An adaptive method based on nodal-patch refinement leads to an asymptotic error reduction property for the computed sequence of simple eigenvalues and eigenfunctions. This justifies the use of the proven saturation property for a class of reliable and efficient hierarchical a posteriori error estimators. Numerical experiments confirm that the saturation property is present even for very coarse meshes for many examples; in other cases the smallness assumption on the initial mesh may be severe. KW - eigenvalue KW - eigenfunction KW - partial differential equation KW - adaptive finite element method KW - saturation Y1 - 2012 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/1192 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-11924 ER -