International Journal for Numerical Methods in Engineering · 2013 · 10 citations · 33 references
Numerical AnalysisParameter EstimationEngineeringSpace DiscretizationMultiple ScaleStochastic AnalysisUncertainty ModelingState EstimationStochastic SimulationParameter IdentificationMultiscale AnalysisUncertainty QuantificationMonte Carlo ApproximationStochastic ProcessesNumerical SimulationModel AdaptationSystems EngineeringModeling And SimulationEstimation TheoryStatisticsArlequin FrameworkMultiscale MethodsStochastic ModelingRobust ModelingError EstimationMonte Carlo MethodModel UncertaintyMultiscale Modeling
SUMMARY 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. By 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. Copyright © 2013 John Wiley & Sons, Ltd.
33