Benchmark results for testing adaptive finite element eigenvalue procedures part 2 (conforming eigenvector and eigenvalue estimates)

Giani, S.; Grubišić, L.; Ovall, J.S.

Abstract

We present an hp-adaptive continuous Galerkin (hp-CG) method for approximating eigenvalues of elliptic operators, and demonstrate its utility on a collection of benchmark problems having features seen in many important practical applications—for example, high-contrast discontinuous coefficients giving rise to eigenfunctions with reduced regularity. In this continuation of our benchmark study, we concentrate on providing reliability estimates for assessing eigenfunction/invariant subspace error. In particular, we use these estimates to justify the observed robustness of eigenvalue error estimates in the presence of repeated or clustered eigenvalues. We also indicate a means for obtaining efficiency estimates from the available efficiency estimates for the associated boundary value (source) problem. As in the first part of the paper we provide extensive numerical tests for comparison with other high-order methods and also extend the list of analyzed benchmark problems.

Citation

Giani, S., Grubišić, L., & Ovall, J. (2016). Benchmark results for testing adaptive finite element eigenvalue procedures part 2 (conforming eigenvector and eigenvalue estimates). Applied Numerical Mathematics, 102, 1-16. https://doi.org/10.1016/j.apnum.2015.12.001

• Journal Article Type: Article
• Acceptance Date: Dec 22, 2015
• Online Publication Date: Dec 31, 2015
• Publication Date: Apr 1, 2016
• Deposit Date: May 31, 2016
• Publicly Available Date: Dec 31, 2016
• Journal: Applied Numerical Mathematics
• Print ISSN: 0168-9274
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 102
• Pages: 1-16
• DOI: https://doi.org/10.1016/j.apnum.2015.12.001
• Public URL: https://durham-repository.worktribe.com/output/1410873