Uncertainty quantification with adaptive mesh refinement in a chemical system

L. Mathelin*, O. P. Le Maître

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

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. A 8-D uncertain problem arises which solution is intractable without a specific strategy while the present technique is shown to perform well and at a reasonable computational cost.

Original languageEnglish (US)
Title of host publicationProceedings of the 6th International Conference on Engineering Computational Technology
StatePublished - 2008
Externally publishedYes
Event6th International Conference on Engineering Computational Technology, ECT 2008 - Athens, Greece
Duration: Sep 2 2008Sep 5 2008

Other

Other6th International Conference on Engineering Computational Technology, ECT 2008
CountryGreece
CityAthens
Period09/2/0809/5/08

Keywords

  • Adaptive mesh refinement
  • Error analysis
  • Polynomial chaos
  • Refinement scheme
  • Stochastic finite element method
  • Uncertainty quantification

ASJC Scopus subject areas

  • Computer Science(all)

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