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| URI | http://purl.tuc.gr/dl/dias/676E5713-E83C-481B-B858-A77E62ABBD13 | - |
| Αναγνωριστικό | https://doi.org/10.1093/imanum/dri044 | - |
| Γλώσσα | en | - |
| Μέγεθος | 22 pages | en |
| Τίτλος | Reduced-basis output bound methods for parabolic problems | en |
| Δημιουργός | Rovas Dimitrios | en |
| Δημιουργός | Ροβας Δημητριος | el |
| Δημιουργός | Maday, Yvon, 1957- | en |
| Δημιουργός | L. Machiels | en |
| Εκδότης | The author | en |
| Περίληψη | In this paper, we extend reduced-basis output bound methods developed earlier for elliptic problems, to problems described by ‘parameterized parabolic’ partial differential equations. The essential new ingredient and the novelty of this paper consist in the presence of time in the formulation and solution of the problem. First, without assuming a time discretization, a reduced-basis procedure is presented to ‘efficiently’ compute accurate approximations to the solution of the parabolic problem and ‘relevant’ outputs of interest. In addition, we develop an error estimation procedure to ‘a posteriori validate’ the accuracy of our output predictions. Second, using the discontinuous Galerkin method for the temporal discretization, the reduced-basis method and the output bound procedure are analysed for the semi-discrete case. In both cases the reduced-basis is constructed by taking ‘snapshots’ of the solution both in time and in the parameters: in that sense the method is close to Proper Orthogonal Decomposition (POD). | en |
| Τύπος | Peer-Reviewed Journal Publication | en |
| Τύπος | Δημοσίευση σε Περιοδικό με Κριτές | el |
| Άδεια Χρήσης | http://creativecommons.org/licenses/by/4.0/ | en |
| Ημερομηνία | 2015-10-17 | - |
| Ημερομηνία Δημοσίευσης | 2006 | - |
| Θεματική Κατηγορία | Greek mathematics | en |
| Θεματική Κατηγορία | mathematics greek | en |
| Θεματική Κατηγορία | greek mathematics | en |
| Βιβλιογραφική Αναφορά | D.V. Rovas, L. Machiels, Y. Maday ," Reduced-basis output bound methods for parabolic problems," IMA j. of num. anal. ,vol.26,no.3 ,pp. 423-445.doi:10.1093/imanum/dri044 | en |
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