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Spectral approximations by the HDG method

Author(s)
Li, Fengyan; Gopalakrishnan, Jay; Peraire, Jaime; Nguyen, Ngoc Cuong
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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.
Date issued
2014-12
URI
http://hdl.handle.net/1721.1/107272
Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
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
ISSN
0025-5718
1088-6842

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