A posteriori error estimation and adaptive strategy for the control of MsFEM computations

Ludovic Chamoin 1, 2 Frederic Legoll 3, 2
2 MATHERIALS - MATHematics for MatERIALS
CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique, Inria de Paris
Abstract : We introduce quantitative and robust tools to control the numerical accuracy in simulations performed using the Multiscale Finite Element Method (MsFEM). First, we propose a guaranteed and fully computable a posteriori error estimate for the global error measured in the energy norm. It is based on dual analysis and the Constitutive Relation Error (CRE) concept, with recovery of equilibrated fluxes from the approximate MsFEM solution. Second, the estimate is split into several indicators, associated to the various MsFEM error sources, in order to drive an adaptive procedure. The overall strategy thus enables to automatically identify an appropriate trade-off between accuracy and computational cost in the MsFEM numerical simulations. Furthermore, the strategy is compatible with the offline/online paradigm of MsFEM. The performances of our approach are demonstrated on several numerical experiments.
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https://hal.archives-ouvertes.fr/hal-01586825
Contributeur : Frederic Legoll <>
Soumis le : mercredi 13 septembre 2017 - 12:15:51
Dernière modification le : vendredi 22 septembre 2017 - 13:14:59

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  • HAL Id : hal-01586825, version 1
  • ARXIV : 1709.03624

Citation

Ludovic Chamoin, Frederic Legoll. A posteriori error estimation and adaptive strategy for the control of MsFEM computations. 2017. 〈hal-01586825〉

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