An Adaptive Finite Element Method with Asymptotic Saturation for Eigenvalue Problems
Please always quote using this URN:urn:nbn:de:0296-matheon-11924
- 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.
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| Author: | Carsten Carstensen, Joscha Gedicke, Volker Mehrmann, Agnieszka Miedlar |
|---|---|
| URN: | urn:nbn:de:0296-matheon-11924 |
| Referee: | Dietmar Hömberg |
| Document Type: | Preprint, Research Center Matheon |
| Language: | English |
| Date of first Publication: | 2012/12/17 |
| Release Date: | 2012/12/17 |
| Tag: | adaptive finite element method; eigenfunction; eigenvalue; partial differential equation; saturation |
| Institute: | Research Center Matheon |
| Humboldt-Universität zu Berlin | |
| Technische Universität Berlin | |
| MSC-Classification: | 65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N15 Error bounds |
| 65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N25 Eigenvalue problems | |
| 65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods | |
| Preprint Number: | 993 |
