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

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

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
• Public URL: https://durham-repository.worktribe.com/output/1246906