Error estimation and model adaptation for a stochastic-deterministic coupling method based on the Arlequin method

Cédric Zaccardi (1) , Ludovic Chamoin (2) , Régis Cottereau (1) , Hachmi Ben Dhia (1)

1 MSSMat - Laboratoire de mécanique des sols, structures et matériaux
2 LMT - Laboratoire de Mécanique et Technologie

The paper deals with the issue of accuracy for multiscale methods applied to solve stochastic problems. It more precisely focuses on the control of a coupling, performed using the Arlequin framework, between a deterministic continuum model and a stochastic continuum one. Using residual-type estimates and adjoint-based techniques, a strategy for goal-oriented error estimation is presented for this coupling and contributions of various error sources (modeling, space discretization, and Monte Carlo approximation) are assessed. Furthermore, an adaptive strategy is proposed to enhance the quality of outputs of interest obtained by the coupled stochastic-deterministic model. Performance of the proposed approach is illustrated on 1D and 2D numerical experiments.

Mots clés: Multiscale methods; Stochastic Mechanics; Arlequin method; Goal-oriented error estimation; a posteriori error estimation

Domaines: Mécanique des solides [physics.class-ph]; Mécanique des solides [physics.class-ph]

Cédric Zaccardi, Ludovic Chamoin, Régis Cottereau, Hachmi Ben Dhia. Error estimation and model adaptation for a stochastic-deterministic coupling method based on the Arlequin method. International Journal for Numerical Methods in Engineering, 2013, 96 (2), pp.87-109. ⟨10.1002/nme.4540⟩. ⟨hal-00869049⟩