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We apply a proper orthogonal decomposition (POD)\u2013greedy sampling procedure for the stable identification of optimal reduced basis spaces, and we develop a rigorous finite-time a posteriori bound for the error in the reduced basis prediction of the two outputs of interest\u2014the optical anisotropy and the first normal stress difference. We present numerical results for stress-conformation hysteresis as a function of Weissenberg number and final time that demonstrate the rapid convergence of the reduced basis approximation and the effectiveness of the a posteriori error bounds.<\/jats:p>","DOI":"10.1137\/090759239","type":"journal-article","created":{"date-parts":[[2010,3,10]],"date-time":"2010-03-10T18:14:29Z","timestamp":1268244869000},"page":"793-817","source":"Crossref","is-referenced-by-count":28,"title":["A Certified Reduced Basis Method for the Fokker\u2013Planck Equation of Dilute Polymeric Fluids: FENE Dumbbells in Extensional Flow"],"prefix":"10.1137","volume":"32","author":[{"given":"David J.","family":"Knezevic","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Anthony T.","family":"Patera","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2010,3,10]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.2514\/3.7539"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jnnfm.2006.07.007"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1016\/j.jnnfm.2007.03.009"},{"key":"R4","doi-asserted-by":"crossref","unstructured":"D. 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