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}
}
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
Highly Cited
This paper has 41 citations. REVIEW CITATIONS

Citations

Publications citing this paper.
Showing 1-10 of 14 extracted citations

A framework of verified eigenvalue bounds for self-adjoint differential operators

Applied Mathematics and Computation • 2015
View 4 Excerpts
Highly Influenced

Guaranteed lower eigenvalue bounds for the biharmonic equation

Numerische Mathematik • 2014
View 12 Excerpts
Highly Influenced

ASYMPTOTIC EXACTNESS OF THE LEAST-SQUARES FINITE ELEMENT RESIDUAL \ast

FINITE ELEMENT RESIDUALast, CARSTEN CARSTENSENdagger AND, JOHANNES STORNddagger
2018
View 1 Excerpt

References

Publications referenced by this paper.
Showing 1-10 of 26 references