New advances in robust goal-oriented error estimation for FE simulations

Abstract : Research and engineering activities for verification are currently turning to robust goal-oriented error estimation methods. These provide for an effective mean of dealing with the control and assessment of the numerical quality of specific quantities of interest. A prevailing concern is the derivation of guaranteed and accurate error bounds on such local quantities. In this framework, a general method, based on well-known robust global error estimation methods and extraction techniques, has been the subject of several research works. It involves the accurate resolution of an auxiliary problem, likewise called adjoint (or mirror in the non-linear case) problem, in order to achieve sharp local error bounds. Nevertheless, this classical bounding technique may lead to imprecise error bounds in some practical situations, especially when the main contributions to the discretization errors related to both reference and auxiliary problems are not located in the same region. Therefore, performances of the classical bounding technique strongly depend on the considered zone of interest, since the most concentrated error region associated to the auxiliary problem usually surrounds this one. In this talk, we first review the classical bounding technique and highlight its main aforementioned drawback. Then, we propose and study two new improvements in order to fill this gap in the robust bounding of linear quantities of interest. These improvements rely on original and forward-looking tools, such as homothetic domains properties, to treat the zone of interest separately from the remainder of the structure, leading to higher quality error bounds. We discuss these proposed alternative bounding techniques and couple them with handbook techniques which allow to handle truly pointwise quantities of interest. The principle of handbook techniques enables to introduce enrichment functions into the resolution of the auxiliary problem. The enrichment functions are applied locally through a partition of unity method (PUM) and correspond to (quasi-)exact solutions of the auxiliary problem. Several two- and three-dimensional numerical experiments are presented to clearly demonstrate the interest and effectivity of the two enhanced techniques.
Type de document :
Communication dans un congrès
10th World Congress on Computational Mechanics (WCCM X), Jul 2012, São Paulo, Brazil. 2012, 〈http://www.wccm2012.com〉
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https://hal.archives-ouvertes.fr/hal-01056927
Contributeur : Florent Pled <>
Soumis le : vendredi 29 août 2014 - 08:52:50
Dernière modification le : jeudi 22 novembre 2018 - 14:25:27

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  • HAL Id : hal-01056927, version 1

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Florent Pled, Ludovic Chamoin, Pierre Ladevèze. New advances in robust goal-oriented error estimation for FE simulations. 10th World Congress on Computational Mechanics (WCCM X), Jul 2012, São Paulo, Brazil. 2012, 〈http://www.wccm2012.com〉. 〈hal-01056927〉

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