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dc.contributor.authorNguyen, Ngoc Cuong
dc.contributor.authorRozza, Gianluigi
dc.contributor.authorPatera, Anthony T.
dc.date.accessioned2013-09-27T16:37:16Z
dc.date.available2013-09-27T16:37:16Z
dc.date.issued2009-06
dc.date.submitted2009-04
dc.identifier.issn0008-0624
dc.identifier.issn1126-5434
dc.identifier.urihttp://hdl.handle.net/1721.1/81221
dc.description.abstractIn 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.sponsorshipUnited States. Air Force Office of Scientific Research (AFOSR Grant FA9550-05-1-0114)en_US
dc.description.sponsorshipUnited States. Air Force Office of Scientific Research (AFOSR Grant FA-9550-07-1-0425)en_US
dc.description.sponsorshipSingapore-MIT Alliance for Research and Technologyen_US
dc.language.isoen_US
dc.publisherSpringer-Verlagen_US
dc.relation.isversionofhttp://dx.doi.org/10.1007/s10092-009-0005-xen_US
dc.rightsCreative Commons Attribution-Noncommercial-Share Alike 3.0en_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/en_US
dc.sourceMIT web domainen_US
dc.titleReduced basis approximation and a posteriori error estimation for the time-dependent viscous Burgers’ equationen_US
dc.typeArticleen_US
dc.identifier.citationNguyen, 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.departmentMassachusetts Institute of Technology. Department of Mechanical Engineeringen_US
dc.contributor.mitauthorNguyen, Ngoc Cuongen_US
dc.contributor.mitauthorPatera, Anthony T.en_US
dc.contributor.mitauthorRozza, Gianluigien_US
dc.relation.journalCalcoloen_US
dc.eprint.versionAuthor's final manuscripten_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/PeerRevieweden_US
dspace.orderedauthorsNguyen, Ngoc-Cuong; Rozza, Gianluigi; Patera, Anthony T.en_US
dc.identifier.orcidhttps://orcid.org/0000-0002-0810-8812
dc.identifier.orcidhttps://orcid.org/0000-0002-2631-6463
mit.licenseOPEN_ACCESS_POLICYen_US
mit.metadata.statusComplete


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