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Reduced-basis output bound methods for parabolic problems

Rovas Dimitrios, Maday, Yvon, 1957-, L. Machiels

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URIhttp://purl.tuc.gr/dl/dias/676E5713-E83C-481B-B858-A77E62ABBD13-
Αναγνωριστικόhttps://doi.org/10.1093/imanum/dri044-
Γλώσσαen-
Μέγεθος22 pagesen
ΤίτλοςReduced-basis output bound methods for parabolic problemsen
ΔημιουργόςRovas Dimitriosen
ΔημιουργόςΡοβας Δημητριοςel
ΔημιουργόςMaday, Yvon, 1957-en
Δημιουργός L. Machielsen
ΕκδότηςThe authoren
ΠερίληψηIn 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
ΤύποςPeer-Reviewed Journal Publicationen
ΤύποςΔημοσίευση σε Περιοδικό με Κριτέςel
Άδεια Χρήσηςhttp://creativecommons.org/licenses/by/4.0/en
Ημερομηνία2015-10-17-
Ημερομηνία Δημοσίευσης2006-
Θεματική ΚατηγορίαGreek mathematicsen
Θεματική Κατηγορίαmathematics greeken
Θεματική Κατηγορίαgreek mathematicsen
Βιβλιογραφική ΑναφοράD.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/dri044en

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