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

Giani, Stefano; Grubišic, Luka; Hakula, Harri; Ovall, Jeffrey S.

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Authors

Luka Grubišic

Harri Hakula

Jeffrey S. Ovall



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.

Citation

Giani, S., Grubišic, L., Hakula, H., & Ovall, J. S. (2021). A Posteriori Error Estimates for Elliptic Eigenvalue Problems Using Auxiliary Subspace Techniques. Journal of Scientific Computing, 88(3), Article 55. https://doi.org/10.1007/s10915-021-01572-2

Journal Article Type Article
Acceptance Date Jun 20, 2021
Online Publication Date Jul 20, 2021
Publication Date 2021-09
Deposit Date Jun 21, 2021
Publicly Available Date Jun 21, 2021
Journal Journal of Scientific Computing
Print ISSN 0885-7474
Electronic ISSN 1573-7691
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 88
Issue 3
Article Number 55
DOI https://doi.org/10.1007/s10915-021-01572-2

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Copyright Statement
This is a post-peer-review, pre-copyedit version of an article published in Journal of Scientific Computing. The final authenticated version is available online at: https://doi.org/10.1007/s10915-021-01572-2





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