Uncertainty quantification in a chemical system using error estimate-based mesh adaption

This paper describes a rigorous a posteriori error analysis for the stochastic solution of non-linear uncertain chemical models. The dual-based a posteriori stochastic error analysis extends the methodology developed in the deterministic finite elements context to stochastic discretization framework...

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Bibliographic Details
Published in:Theoretical and computational fluid dynamics 2012-10, Vol.26 (5), p.415-434
Main Authors: Mathelin, Lionel, Le Maître, Olivier P.
Format: Article
Language:English
Subjects:
Chaos theory
Classical and Continuum Physics
Computational Science and Engineering
Discretization
Engineering
Engineering Fluid Dynamics
Error analysis
Error analysis (Mathematics)
Estimates
Finite element analysis
Fluid dynamics
Fluid flow
Mathematical models
Mathematical research
Methodology
Original Article
Permissible error
Stochastic analysis
Stochastic models
Stochasticity
Strategy
Uncertainty
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Summary:This paper describes a rigorous a posteriori error analysis for the stochastic solution of non-linear uncertain chemical models. The dual-based a posteriori stochastic error analysis extends the methodology developed in the deterministic finite elements context to stochastic discretization frameworks. It requires the resolution of two additional (dual) problems to yield the local error estimate. The stochastic error estimate can then be used to adapt the stochastic discretization. Different anisotropic refinement strategies are proposed, leading to a cost-efficient tool suitable for multi-dimensional problems of moderate stochastic dimension. The adaptive strategies allow both for refinement and coarsening of the stochastic discretization, as needed to satisfy a prescribed error tolerance. The adaptive strategies were successfully tested on a model for the hydrogen oxidation in supercritical conditions having 8 random parameters. The proposed methodologies are however general enough to be also applicable for a wide class of models such as uncertain fluid flows.
ISSN:0935-4964
1432-2250
DOI:10.1007/s00162-010-0210-x