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Reduced-basis output bound methods for parabolic problems

Rovas, DV; Machiels, L; Maday, Y; (2006) Reduced-basis output bound methods for parabolic problems. IMA Journal of Numerical Analysis , 26 (3) pp. 423-445. 10.1093/imanum/dri044. Green open access

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Abstract

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).

Type: Article
Title: Reduced-basis output bound methods for parabolic problems
Open access status: An open access version is available from UCL Discovery
DOI: 10.1093/imanum/dri044
Publisher version: https://doi.org/10.1093/imanum/dri044
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of the Built Environment
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of the Built Environment > Bartlett School Env, Energy and Resources
URI: https://discovery.ucl.ac.uk/id/eprint/10063071
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