A Posteriori Error Estimates for Elliptic Eigenvalue Problems Using Auxiliary Subspace Techniques

Stefano Giani, Luka Grubišić, Harri Hakula, Jeffrey S. Ovall*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

Abstract

We propose an a posteriori error estimator for high-order p- or hp-finite element discretizations of selfadjoint linear elliptic eigenvalue problems that is appropriate for estimating the error in the approximation of an eigenvalue cluster and the corresponding invariant subspace. The estimator is based on the computation of approximate error functions in a space that complements the one in which the approximate eigenvectors were computed. These error functions are used to construct estimates of collective measures of error, such as the Hausdorff distance between the true and approximate clusters of eigenvalues, and the subspace gap between the corresponding true and approximate invariant subspaces. Numerical experiments demonstrate the practical effectivity of the approach.

Original languageEnglish
Article number55
JournalJOURNAL OF SCIENTIFIC COMPUTING
Volume88
Issue number3
DOIs
Publication statusPublished - Sep 2021
MoE publication typeA1 Journal article-refereed

Keywords

  • A posteriori error estimation
  • Eigenvalue clusters
  • Eigenvalue problems
  • Finite elements

Fingerprint

Dive into the research topics of 'A Posteriori Error Estimates for Elliptic Eigenvalue Problems Using Auxiliary Subspace Techniques'. Together they form a unique fingerprint.

Cite this