dc.contributor.author | Yano, Masayuki | |
dc.contributor.author | Patera, Anthony T. | |
dc.contributor.author | Urban, Karsten | |
dc.date.accessioned | 2015-07-07T16:33:14Z | |
dc.date.available | 2015-07-07T16:33:14Z | |
dc.date.issued | 2014-02 | |
dc.date.submitted | 2013-07 | |
dc.identifier.issn | 0218-2025 | |
dc.identifier.issn | 1793-6314 | |
dc.identifier.uri | http://hdl.handle.net/1721.1/97700 | |
dc.description.abstract | We present a space-time interpolation-based certified reduced basis method for Burgers' equation over the spatial interval (0, 1) and the temporal interval (0, T] parametrized with respect to the Peclet number. We first introduce a Petrov–Galerkin space-time finite element discretization which enjoys a favorable inf–sup constant that decreases slowly with Peclet number and final time T. We then consider an hp interpolation-based space-time reduced basis approximation and associated Brezzi–Rappaz–Raviart a posteriori error bounds. We describe computational offline–online decomposition procedures for the three key ingredients of the error bounds: the dual norm of the residual, a lower bound for the inf–sup constant, and the space-time Sobolev embedding constant. Numerical results demonstrate that our space-time formulation provides improved stability constants compared to classical L[superscript 2]-error estimates; the error bounds remain sharp over a wide range of Peclet numbers and long integration times T, in marked contrast to the exponentially growing estimate of the classical formulation for high Peclet number cases. | en_US |
dc.description.sponsorship | United States. Air Force Office of Scientific Research. Multidisciplinary University Research Initiative (Grant FA9550-09-1-0613) | en_US |
dc.description.sponsorship | United States. Office of Naval Research (Grant N00014-11-1-0713) | en_US |
dc.description.sponsorship | Deutsche Forschungsgemeinschaft (Ur-63/9) | en_US |
dc.description.sponsorship | Deutsche Forschungsgemeinschaft (GrK1100) | en_US |
dc.language.iso | en_US | |
dc.publisher | World Scientific | en_US |
dc.relation.isversionof | http://dx.doi.org/10.1142/S0218202514500110 | en_US |
dc.rights | Creative Commons Attribution-Noncommercial-Share Alike | en_US |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-sa/4.0/ | en_US |
dc.source | Other univ. web domain | en_US |
dc.title | A space-time certified reduced basis method for Burgers' equation | en_US |
dc.title.alternative | A space-time hp-interpolation-based certified reduced basis method for Burgers' equation | en_US |
dc.type | Article | en_US |
dc.identifier.citation | Yano, Masayuki, Anthony T. Patera, and Karsten Urban. “A Space-Time Hp-Interpolation-Based Certified Reduced Basis Method for Burgers’ Equation.” Math. Models Methods Appl. Sci. 24, no. 09 (August 2014): 1903–1935. | en_US |
dc.contributor.department | Massachusetts Institute of Technology. Department of Mechanical Engineering | en_US |
dc.contributor.mitauthor | Yano, Masayuki | en_US |
dc.contributor.mitauthor | Patera, Anthony T. | en_US |
dc.relation.journal | Mathematical Models and Methods in Applied Sciences | en_US |
dc.eprint.version | Original manuscript | en_US |
dc.type.uri | http://purl.org/eprint/type/JournalArticle | en_US |
eprint.status | http://purl.org/eprint/status/NonPeerReviewed | en_US |
dspace.orderedauthors | Yano, Masayuki; Patera, Anthony T.; Urban, Karsten | en_US |
dc.identifier.orcid | https://orcid.org/0000-0002-8323-9054 | |
dc.identifier.orcid | https://orcid.org/0000-0002-2631-6463 | |
mit.license | OPEN_ACCESS_POLICY | en_US |
mit.metadata.status | Complete | |