dc.contributor.author | Nguyen, Ngoc Cuong | |
dc.contributor.author | Rozza, Gianluigi | |
dc.contributor.author | Patera, Anthony T. | |
dc.date.accessioned | 2013-09-27T16:37:16Z | |
dc.date.available | 2013-09-27T16:37:16Z | |
dc.date.issued | 2009-06 | |
dc.date.submitted | 2009-04 | |
dc.identifier.issn | 0008-0624 | |
dc.identifier.issn | 1126-5434 | |
dc.identifier.uri | http://hdl.handle.net/1721.1/81221 | |
dc.description.abstract | In this paper we present rigorous a posteriori L 2 error bounds for reduced basis approximations of the unsteady viscous Burgers’ equation in one space dimension. The a posteriori error estimator, derived from standard analysis of the error-residual equation, comprises two key ingredients—both of which admit efficient Offline-Online treatment: the first is a sum over timesteps of the square of the dual norm of the residual; the second is an accurate upper bound (computed by the Successive Constraint Method) for the exponential-in-time stability factor. These error bounds serve both Offline for construction of the reduced basis space by a new POD-Greedy procedure and Online for verification of fidelity. The a posteriori error bounds are practicable for final times (measured in convective units) T≈O(1) and Reynolds numbers ν[superscript −1]≫1; we present numerical results for a (stationary) steepening front for T=2 and 1≤ν[superscript −1]≤200. | en_US |
dc.description.sponsorship | United States. Air Force Office of Scientific Research (AFOSR Grant FA9550-05-1-0114) | en_US |
dc.description.sponsorship | United States. Air Force Office of Scientific Research (AFOSR Grant FA-9550-07-1-0425) | en_US |
dc.description.sponsorship | Singapore-MIT Alliance for Research and Technology | en_US |
dc.language.iso | en_US | |
dc.publisher | Springer-Verlag | en_US |
dc.relation.isversionof | http://dx.doi.org/10.1007/s10092-009-0005-x | en_US |
dc.rights | Creative Commons Attribution-Noncommercial-Share Alike 3.0 | en_US |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-sa/3.0/ | en_US |
dc.source | MIT web domain | en_US |
dc.title | Reduced basis approximation and a posteriori error estimation for the time-dependent viscous Burgers’ equation | en_US |
dc.type | Article | en_US |
dc.identifier.citation | Nguyen, Ngoc-Cuong, Gianluigi Rozza, and Anthony T. Patera. Reduced Basis Approximation and a Posteriori Error Estimation for the Time-dependent Viscous Burgers’ Equation. Calcolo 46, no. 3 (September 30, 2009): 157-185. | en_US |
dc.contributor.department | Massachusetts Institute of Technology. Department of Mechanical Engineering | en_US |
dc.contributor.mitauthor | Nguyen, Ngoc Cuong | en_US |
dc.contributor.mitauthor | Patera, Anthony T. | en_US |
dc.contributor.mitauthor | Rozza, Gianluigi | en_US |
dc.relation.journal | Calcolo | en_US |
dc.eprint.version | Author's final manuscript | 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 | Nguyen, Ngoc-Cuong; Rozza, Gianluigi; Patera, Anthony T. | en_US |
dc.identifier.orcid | https://orcid.org/0000-0002-0810-8812 | |
dc.identifier.orcid | https://orcid.org/0000-0002-2631-6463 | |
mit.license | OPEN_ACCESS_POLICY | en_US |
mit.metadata.status | Complete | |