Guaranteed lower bounds for eigenvalues

@article{Carstensen2014GuaranteedLB,
  title={Guaranteed lower bounds for eigenvalues},
  author={Carsten Carstensen and Joscha Gedicke},
  journal={Math. Comput.},
  year={2014},
  volume={83},
  pages={2605-2629}
}

• Carsten Carstensen, Joscha Gedicke
• Published 2014 in Math. Comput.
• DOI:10.1090/S0025-5718-2014-02833-0

This paper introduces fully computable two-sided bounds on the eigenvalues of the Laplace operator on arbitrarily coarse meshes based on some approximation of the corresponding eigenfunction in the nonconforming Crouzeix-Raviart finite element space plus some postprocessing. The efficiency of the guaranteed error bounds involves the global mesh-size and is proven for the large class of graded meshes. Numerical examples demonstrate the reliability of the guaranteed error control even with an… CONTINUE READING

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