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Adaptive guaranteed lower eigenvalue bounds with optimal convergence rates
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- معلومة اضافية
- بيانات النشر:
Humboldt-Universität zu Berlin
- الموضوع:
2023
- Collection:
Open-Access-Publikationsserver der Humboldt-Universität: edoc-Server
- نبذة مختصرة :
Guaranteed lower Dirichlet eigenvalue bounds (GLB) can be computed for the m-th Laplace operator with a recently introduced extra-stabilized nonconforming Crouzeix–Raviart (m = 1) or Morley (m = 2) finite element eigensolver. Striking numerical evidence for the superiority of a new adaptive eigensolver motivates the convergence analysis in this paper with a proof of optimal convergence rates of the GLB towards a simple eigenvalue. The proof is based on (a generalization of) known abstract arguments entitled as the axioms of adaptivity. Beyond the known a priori convergence rates, a medius analysis is enfolded in this paper for the proof of best-approximation results. This and subordinated L2 error estimates for locally refined triangulations appear of independent interest. The analysis of optimal convergence rates of an adaptive mesh-refining algorithm is performed in 3D and highlights a new version of discrete reliability. ; Peer Reviewed
- File Description:
application/pdf
- ISSN:
0945-3245
- Relation:
http://edoc.hu-berlin.de/18452/29115; urn:nbn:de:kobv:11-110-18452/29115-5; http://dx.doi.org/10.18452/28468
- الرقم المعرف:
10.18452/28468
- الرقم المعرف:
10.1007/s00211-023-01382-8
- Rights:
(CC BY 4.0) Attribution 4.0 International ; https://creativecommons.org/licenses/by/4.0/
- الرقم المعرف:
edsbas.FBB9EA61
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