Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

Guaranteed lower bounds on eigenvalues of elliptic operators with a hybrid high-order method

Abstract : This paper introduces a novel hybrid high-order (HHO) method to approximate the eigenvalues of a symmetric compact differential operator. The HHO method combines two gradient reconstruction operators by means of a parameter $0<\alpha<1$ and introduces a novel cell-based stabilization operator weighted by a parameter $0<\beta<\infty$. Sufficient conditions on the parameters $\alpha$ and $\beta$ are identified leading to a guaranteed lower bound property for the discrete eigenvalues. Moreover optimal convergence rates are established. Numerical studies for the Dirichlet eigenvalue problem of the Laplacian provide evidence for the superiority of the new lower eigenvalue bounds compared to previously available bounds.
Document type :
Preprints, Working Papers, ...
Complete list of metadata

https://hal.archives-ouvertes.fr/hal-02863599
Contributor : Alexandre Ern <>
Submitted on : Tuesday, August 3, 2021 - 1:24:31 PM
Last modification on : Thursday, August 5, 2021 - 3:12:50 AM

File

HHO_EVP_final.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-02863599, version 4

Collections

Citation

Carsten Carstensen, Alexandre Ern, Sophie Puttkammer. Guaranteed lower bounds on eigenvalues of elliptic operators with a hybrid high-order method. 2021. ⟨hal-02863599v4⟩

Share

Metrics

Record views

41

Files downloads

22