A posteriori error estimation and adaptive strategy for PGD model reduction applied to parametrized linear parabolic problems

Abstract : We define an a posteriori verification procedure that enables to control and certify PGD-based model reduction techniques applied to parametrized linear elliptic or parabolic problems. Using the concept of constitutive relation error, it provides guaranteed and fully computable global/goal-oriented error estimates taking both discretization and PGD truncation errors into account. Splitting the error sources, it also leads to a natural greedy adaptive strategy which can be driven in order to optimize the accuracy of PGD approximations. The focus of the paper is on two technical points: (i) construction of equilibrated fields required to compute guaranteed error bounds; (ii) error splitting and adaptive process when performing PGD-based model reduction. Performances of the proposed verification and adaptation tools are shown on several multi-parameter mechanical problems.
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https://hal.archives-ouvertes.fr/hal-01584532
Contributeur : Ludovic Chamoin <>
Soumis le : lundi 22 janvier 2018 - 14:22:35
Dernière modification le : samedi 23 mars 2019 - 01:29:33
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Ludovic Chamoin, Florent Pled, Pierre-Eric Allier, Pierre Ladevèze. A posteriori error estimation and adaptive strategy for PGD model reduction applied to parametrized linear parabolic problems. Computer Methods in Applied Mechanics and Engineering, Elsevier, 2017, 327, pp.118-146. 〈10.1016/j.cma.2017.08.047〉. 〈hal-01584532〉

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