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arXiv · 1801.07422

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

Ludovic Chamoin·Florent Pled·Pierre-Eric Allier·Pierre Ladevèze
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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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Ludovic Chamoin, Florent Pled, Pierre-Eric Allier, Pierre Ladevèze. 2018-01-23. A posteriori error estimation and adaptive strategy for PGD model reduction applied to parametrized linear parabolic problems. https://doi.org/10.1016/j.cma.2017.08.047

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