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

Lionel Mathelin*, Olivier P. Le Maǐtre

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)415-434
Number of pages20
JournalTheoretical and Computational Fluid Dynamics
Issue number5
StatePublished - Oct 2012
Externally publishedYes


  • Adaptive mesh refinement
  • Error analysis
  • Polynomial Chaos
  • Stochastic finite elements method
  • Uncertainty quantification

ASJC Scopus subject areas

  • Computational Mechanics
  • Condensed Matter Physics
  • General Engineering
  • Fluid Flow and Transfer Processes


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