Hybridization and postprocessing techniques for mixed eigenfunctions

B. Cockburn, J. Gopalakrishnan, F. Li, N. C. Nguyen, J. Peraire

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)857-881
Number of pages25
JournalSIAM Journal on Numerical Analysis
Volume48
Issue number3
DOIs
StatePublished - 2010

Keywords

  • Eigenfunction
  • Hybridization
  • Mixed method
  • Nonlinear eigenvalue
  • Postprocessing
  • Superconvergence

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