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Article
Hybridization and Postprocessing Techniques for Mixed Eigenfunctions
SIAM Journal on Numerical Analysis
  • Bernardo Cockburn, University of Minnesota - Twin Cities
  • Jay Gopalakrishnan, Portland State University
  • F. Li, Rensselaer Polytechnic Institute
  • Ngoc Cuong Nguyen, Massachusetts Institute of Technology
  • Jaume Peraire, Massachusetts Institute of Technology
Document Type
Post-Print
Publication Date
1-1-2010
Subjects
  • Hybridization -- Molecular aspects,
  • Approximation theory,
  • Eigenfunctions
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.
Description

This is an Author's Accepted Manuscript. First Published in SIAM Journal on Numerical Analysis in volume 48 and Issue 3, published by the Society of Industrial and Applied Mathematics (SIAM) . Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.

DOI
10.1137/090765894
Persistent Identifier
http://archives.pdx.edu/ds/psu/10654
Citation Information
Bernardo Cockburn, Jay Gopalakrishnan, F. Li, Ngoc Cuong Nguyen, et al.. "Hybridization and Postprocessing Techniques for Mixed Eigenfunctions" SIAM Journal on Numerical Analysis (2010)
Available at: http://works.bepress.com/jay-gopalakrishnan/79/