Error control for hp -adaptive approximations of semi-definite eigenvalue problems

Giani, S.; Grubišić, L.; Ovall, J.

Abstract

We present reliable TeX-posteriori error estimates for TeX-adaptive finite element approximations of semi-definite eigenvalue/eigenvector problems. Our model problems are motivated by applications in photonic crystal eigenvalue computations. We present detailed numerical experiments confirming our theory and give several benchmark results which could serve the purpose of numerical testing of other adaptive procedures.

Citation

Giani, S., Grubišić, L., & Ovall, J. (2013). Error control for hp -adaptive approximations of semi-definite eigenvalue problems. Computing, 95(1), 235-257. https://doi.org/10.1007/s00607-012-0260-6

• Journal Article Type: Article
• Publication Date: May 1, 2013
• Deposit Date: Feb 12, 2013
• Publicly Available Date: Apr 20, 2015
• Journal: Computing
• Print ISSN: 0010-485X
• Electronic ISSN: 1436-5057
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 95
• Issue: 1
• Pages: 235-257
• DOI: https://doi.org/10.1007/s00607-012-0260-6
• Keywords: Eigenvalue problem, Finite element method, A posteriori error estimates, Primary 65N30, Secondary 65N25, 65N15.
• Related Public URLs: http://eprints.nottingham.ac.uk/1616/1/NEUMANN.pdf