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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-
Identifierhttps://doi.org/10.1093/imanum/dri044-
Languageen-
Extent22 pagesen
TitleReduced-basis output bound methods for parabolic problemsen
CreatorRovas Dimitriosen
CreatorΡοβας Δημητριοςel
CreatorMaday, Yvon, 1957-en
Creator L. Machielsen
PublisherThe authoren
Content SummaryIn 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
Type of ItemPeer-Reviewed Journal Publicationen
Type of ItemΔημοσίευση σε Περιοδικό με Κριτέςel
Licensehttp://creativecommons.org/licenses/by/4.0/en
Date of Item2015-10-17-
Date of Publication2006-
SubjectGreek mathematicsen
Subjectmathematics greeken
Subjectgreek mathematicsen
Bibliographic CitationD.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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