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Table 1 Eigenvalues for a clamped-clamped uniform beam of square section, with thickness d =1 and length L =40

From: Component-based reduced basis for parametrized symmetric eigenproblems

  λ 1 λ 2 λ 3 λ 4
Euler Bernoulli 1.6294e-05 1.2381e-04 4.7583e-04 1.3003e-03
Timoshenko 1.6204e-05 1.2224e-04 4.6524e-04 1.2560e-03
Global FEM 1.6612e-05 1.2489e-04 4.7327e-04 1.2708e-03
SCRBE n A,p=108 1.6612e-05 1.2489e-04 4.7327e-04 1.2708e-03
SCRBE n A,p=20 1.6612e-05 1.2489e-04 4.7327e-04 1.2708e-03
\(\widetilde \Delta \) 1.4418e-06 2.0695e-07 7.9612e-08 9.6913e-08
\(\widehat \Delta \) 5.5488e-03 7.3845e-03 8.4207e-03 7.4811e-03
  λ 5 λ 6 λ 7 λ 8
Euler Bernoulli 2.9016e-03 5.6603e-03
Timoshenko 2.7622e-03 5.2991e-03
Global FEM 2.0732e-03 2.7775e-03 5.2916e-03 6.1912e-03
SCRBE n A,p=108 2.0732e-03 2.7775e-03 5.2916e-03 6.1912e-03
SCRBE n A,p=20 2.0732e-03 2.7775e-03 5.2916e-03 6.1912e-03
\(\widetilde \Delta \) 5.4576e-09 4.1418e-07 1.0262e-06 8.8249e-09
\(\widehat \Delta \) 3.3180e-02 8.3262e-03 8.9995e-03 4.7761e-03
  1. The estimators \(\widetilde \Delta \) and \(\widehat \Delta \) correspond to relative errors. Note that we have eigenvalues of multiplicity two due to the symmetry of the beam square section but we only report distinct eigenvalues in this table.