Reduced-basis output bound methods for parabolic problemsReduced-basis output bound methods for parabolic problems Peer-Reviewed Journal Publication Δημοσίευση σε Περιοδικό με Κριτές 2015-10-172006enIn 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).http://creativecommons.org/licenses/by/4.0/ journal of numerical analysis326423-445 Rovas Dimitrios Ροβας Δημητριος Maday, Yvon, 1957- L. Machiels The author Greek mathematics mathematics greek greek mathematics