Spectral approximations by the HDG method
Name
Peraire_Spectral approximations.pdf
Size
271.02 KB
Format
Adobe PDF
Checksum (MD5)
73eb4038d5aec6630b02dfca7478d142
Author(s)
Li, Fengyan
Gopalakrishnan, Jay
Peraire, Jaime
Nguyen, Ngoc Cuong
Date Issued
December 2014
Journal
Mathematics of Computation
Publisher
American Mathematical Society (AMS)
Citation
Gopalakrishnan, J. et al. “Spectral Approximations by the HDG Method.” Mathematics of Computation 84.293 (2014): 1037–1059. © 2014 American Mathematical Society
Version
Final published version
Abstract
We consider the numerical approximation of the spectrum of a second-order elliptic eigenvalue problem by the hybridizable discontinuous Galerkin (HDG) method. We show for problems with smooth eigenfunctions that the approximate eigenvalues and eigenfunctions converge at the rate 2k+1 and k+1, respectively. Here k is the degree of the polynomials used to approximate the solution, its flux, and the numerical traces. Our numerical studies show that a Rayleigh quotient-like formula applied to certain locally postprocessed approximations can yield eigenvalues that converge faster at the rate 2k + 2 for the HDG method as well as for the Brezzi-Douglas-Marini (BDM) method. We also derive and study a condensed nonlinear eigenproblem for the numerical traces obtained by eliminating all the other variables.
MIT Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
Terms of Use
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.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1090/S0025-5718-2014-02885-8
