An Optimal Adaptive FEM for Eigenvalue Clusters
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- 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.
Verfasserangaben: | Dietmar Gallistl |
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URN: | urn:nbn:de:0296-matheon-12870 |
Gutachter*in: | Volker Mehrmann |
Dokumentart: | Preprint, Forschungszentrum Matheon |
Sprache: | Englisch |
Datum der Erstveröffentlichung: | 14.05.2014 |
Datum der Freischaltung: | 14.05.2014 |
Freies Schlagwort / Tag: | eigenvalue problem, eigenvalue cluster, adaptive finite element method, optimality |
Institut: | Humboldt-Universität zu Berlin |
MSC-Klassifikation: | 65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N12 Stability and convergence of numerical methods |
Preprint-Nummer: | 1059 |