Hybridization and Postprocessing Techniques for Mixed Eigenfunctions
Name
Cockburn-2010-HYBRIDIZATION AND PO.pdf
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Author(s)
Peraire, Jaime
Nguyen, Ngoc Cuong
Cockburn, Bernardo
Gopalakrishnan, Jayadeep
Li, Fengyan
Date Issued
June 2010
Journal
SIAM Journal on Numerical Analysis
Publisher
Society for Industrial and Applied Mathematics
Citation
Cockburn, B. et al. “Hybridization and Postprocessing Techniques for Mixed Eigenfunctions.” SIAM Journal on Numerical Analysis 48.3 (2010): 857. c2010 Society for Industrial and Applied Mathematics
Version
Final published version
Abstract
We introduce hybridization and postprocessing techniques for the Raviart–Thomas approximation of second-order elliptic eigenvalue problems. Hybridization reduces the Raviart–Thomas approximation to a condensed eigenproblem. The condensed eigenproblem is nonlinear, but smaller than the original mixed approximation. We derive multiple iterative algorithms for solving the condensed eigenproblem and examine their interrelationships and convergence rates. An element-by-element postprocessing technique to improve accuracy of computed eigenfunctions is also presented. We prove that a projection of the error in the eigenspace approximation by the mixed method (of any order) superconverges and that the postprocessed eigenfunction approximations converge faster for smooth eigenfunctions. Numerical experiments using a square and an L-shaped domain illustrate the theoretical results.
MIT Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1137/090765894
