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arXiv · 1207.1181

Spectral approximations by the HDG method

J. Gopalakrishnan·F. Li·N. -C. Nguyen·J. Peraire
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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.

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J. Gopalakrishnan, F. Li, N. -C. Nguyen, J. Peraire. 2012-07-05. Spectral approximations by the HDG method. https://doi.org/10.1090/s0025-5718-2014-02885-8

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