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Adaptive guaranteed lower eigenvalue bounds with optimal convergence rates.
- Source :
- Numerische Mathematik; Feb2024, Vol. 156 Issue 1, p1-38, 38p
- Publication Year :
- 2024
-
Abstract
- 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 L 2 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- GENERALIZATION
AXIOMS
A priori
ARGUMENT
ALGORITHMS
Subjects
Details
- Language :
- English
- ISSN :
- 0029599X
- Volume :
- 156
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Numerische Mathematik
- Publication Type :
- Academic Journal
- Accession number :
- 175234482
- Full Text :
- https://doi.org/10.1007/s00211-023-01382-8