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L. Mathelin, O.P. Le Maître, "Uncertainty Quantification with Adaptive Mesh Refinement in a Chemical System", in M. Papadrakakis, B.H.V. Topping, (Editors), "Proceedings of the Sixth International Conference on Engineering Computational Technology", Civil-Comp Press, Stirlingshire, UK, Paper 15, 2008. doi:10.4203/ccp.89.15

Keywords: uncertainty quantification, error analysis, stochastic finite element method, refinement scheme, polynomial chaos, adaptive mesh refinement.

Summary

This paper presents an efficient a posteriori error analysis for stochastic PDEs. While adaptive methods have already been used to quantify uncertainty of large scale and/or high dimensional problems, no rigorous criterion for the adaption strategy exists and the different techniques all rely on heuristic considerations. An extension of the dual-based a posteriori error analysis is here presented in the uncertainty quantification framework. The method allows both for refinement and coarsening of the stochastic discretization, leading to an efficient tool. A stiff chemical system with uncertain reactions rates is considered to illustrate the technique. An eight-dimensional uncertainty problem arises where the solution is intractable without a specific strategy while the present technique is shown to perform well and with a reasonable computational cost.

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 89 PROCEEDINGS OF THE SIXTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY Edited by: M. Papadrakakis and B.H.V. Topping Paper 15 Uncertainty Quantification with Adaptive Mesh Refinement in a Chemical System L. Mathelin and O.P. Le Maître Computer Sciences Laboratory for Mechanics and Engineering Sciences (LIMSI), Orsay, France doi:10.4203/ccp.89.15 purchase the full-text of this paper Full Bibliographic Reference for this paper L. Mathelin, O.P. Le Maître, "Uncertainty Quantification with Adaptive Mesh Refinement in a Chemical System", in M. Papadrakakis, B.H.V. Topping, (Editors), "Proceedings of the Sixth International Conference on Engineering Computational Technology", Civil-Comp Press, Stirlingshire, UK, Paper 15, 2008. doi:10.4203/ccp.89.15 Keywords: uncertainty quantification, error analysis, stochastic finite element method, refinement scheme, polynomial chaos, adaptive mesh refinement. Summary This paper presents an efficient a posteriori error analysis for stochastic PDEs. While adaptive methods have already been used to quantify uncertainty of large scale and/or high dimensional problems, no rigorous criterion for the adaption strategy exists and the different techniques all rely on heuristic considerations. An extension of the dual-based a posteriori error analysis is here presented in the uncertainty quantification framework. The method allows both for refinement and coarsening of the stochastic discretization, leading to an efficient tool. A stiff chemical system with uncertain reactions rates is considered to illustrate the technique. An eight-dimensional uncertainty problem arises where the solution is intractable without a specific strategy while the present technique is shown to perform well and with a reasonable computational cost. purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £95 +P&P)
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