Spectral approximations by the HDG method
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.
Cite
@article{arxiv.1207.1181,
title = {Spectral approximations by the HDG method},
author = {J. Gopalakrishnan and F. Li and N. -C. Nguyen and J. Peraire},
journal= {arXiv preprint arXiv:1207.1181},
year = {2015}
}