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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
Contributor : Ludovic Chamoin <>
Submitted on : Monday, January 22, 2018 - 2:22:35 PM
Last modification on : Thursday, March 19, 2020 - 11:52:04 AM
Document(s) archivé(s) le : Monday, April 23, 2018 - 12:41:41 PM

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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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