dc.contributor.author | Li, Fengyan | |
dc.contributor.author | Gopalakrishnan, Jay | |
dc.contributor.author | Peraire, Jaime | |
dc.contributor.author | Nguyen, Ngoc Cuong | |
dc.date.accessioned | 2017-03-09T21:38:58Z | |
dc.date.available | 2017-03-09T21:38:58Z | |
dc.date.issued | 2014-12 | |
dc.date.submitted | 2012-07 | |
dc.identifier.issn | 0025-5718 | |
dc.identifier.issn | 1088-6842 | |
dc.identifier.uri | http://hdl.handle.net/1721.1/107272 | |
dc.description.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. | en_US |
dc.description.sponsorship | National Science Foundation (U.S.) (Grants DMS-1211635, DMS-1318916, and CAREER Award DMS-0847241) | en_US |
dc.description.sponsorship | Alfred P. Sloan Foundation (Research Fellowship) | en_US |
dc.description.sponsorship | United States. Air Force Office of Scientific Research (Grant FA9550-12-0357) | en_US |
dc.language.iso | en_US | |
dc.publisher | American Mathematical Society (AMS) | en_US |
dc.relation.isversionof | https://doi.org/10.1090/S0025-5718-2014-02885-8 | en_US |
dc.rights | 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. | en_US |
dc.source | American Mathematical Society | en_US |
dc.title | Spectral approximations by the HDG method | en_US |
dc.type | Article | en_US |
dc.identifier.citation | Gopalakrishnan, J. et al. “Spectral Approximations by the HDG Method.” Mathematics of Computation 84.293 (2014): 1037–1059. © 2014 American Mathematical Society | en_US |
dc.contributor.department | Massachusetts Institute of Technology. Department of Aeronautics and Astronautics | en_US |
dc.contributor.mitauthor | Peraire, Jaime | |
dc.contributor.mitauthor | Nguyen, Ngoc Cuong | |
dc.relation.journal | Mathematics of Computation | en_US |
dc.eprint.version | Final published version | en_US |
dc.type.uri | http://purl.org/eprint/type/JournalArticle | en_US |
eprint.status | http://purl.org/eprint/status/PeerReviewed | en_US |
dspace.orderedauthors | Gopalakrishnan, J,; Li, F.; Nguyen, N.-C.; Peraire, J. | en_US |
dspace.embargo.terms | N | en_US |
dc.identifier.orcid | https://orcid.org/0000-0002-8556-685X | |
mit.license | PUBLISHER_POLICY | en_US |