Adaptive guaranteed lower eigenvalue bounds with optimal convergence rates
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 eig...
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Veröffentlicht in: | Numerische Mathematik 2024-02, Vol.156 (1), p.1-38 |
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Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | 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. |
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ISSN: | 0029-599X 0945-3245 |
DOI: | 10.1007/s00211-023-01382-8 |