TY - GEN A1 - Mehrmann, Volker A1 - Miedlar, Agnieszka T1 - Adaptive solution of elliptic PDE-eigenvalue problems. Part I: Eigenvalues N2 - We consider a new adaptive finite element (AFEM) algorithm for elliptic PDE-eigenvalue problems. In contrast to other approaches we incorporate the iterative solution of the resulting finite dimensional algebraic eigenvalue problems into the adaptation process. In this way we can balance the costs of the adaption process for the mesh with the costs for the iterative eigenvalue method. We present error estimates that incorporate the discretization errors, approximation errors in the eigenvalue solver and roundoff errors and use these for the adaptation process. We show that for the adaptation process it is possible to restrict to very few iterations of a Krylov subspace solver for the eigenvalue problem on coarse meshes. We present several examples and show that this new approach achieves much better complexity than previous AFEM approaches which assume that the algebraic eigenvalue problem is solved to full accuracy. KW - eigenvalue problem KW - finite element method (FEM) KW - adaptive finite element method (AFEM) KW - elliptic eigenvalue problem KW - Krylov subspace method Y1 - 2009 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/565 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-5650 ER -