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On the robustness of variational multiscale error estimators for the forward propagation of uncertainty

Publication ,  Journal Article
Colomés, O; Scovazzi, G; Guilleminot, J
Published in: Computer Methods in Applied Mechanics and Engineering
December 1, 2018

The numerical simulation of physical phenomena and engineering problems can be affected by numerical errors and various types of uncertainties. Characterizing the former in computational frameworks involving system parameter uncertainties becomes a key issue. In this work, we study the behavior of new variational multiscale (VMS) error estimators for the propagation of parametric uncertainties in a Convection–Diffusion–Reaction (CDR) problem. A sensitivity analysis is performed to assess the performance of the error estimator with respect to the mesh discretization and physical parameters (here, the viscosity value and advection velocity). Three different manufactured analytical solutions are considered as benchmarking tests. Next, the performance of the VMS error estimators is evaluated for the CDR problem with uncertain input parameters. For this purpose, two probabilistic models are constructed for the viscosity and advection direction, and the uncertainties are propagated using a polynomial chaos expansion approach. A convergence analysis is specifically carried out for different configurations, corresponding to regimes where the CDR operator is either smooth or non-smooth. An assessment of the proposed error estimator is finally conducted for the three tests, considering both the viscous- and convection-dominated regimes.

Duke Scholars

Published In

Computer Methods in Applied Mechanics and Engineering

DOI

ISSN

0045-7825

Publication Date

December 1, 2018

Volume

342

Start / End Page

384 / 413

Related Subject Headings

  • Applied Mathematics
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 01 Mathematical Sciences
 

Citation

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Colomés, O., Scovazzi, G., & Guilleminot, J. (2018). On the robustness of variational multiscale error estimators for the forward propagation of uncertainty. Computer Methods in Applied Mechanics and Engineering, 342, 384–413. https://doi.org/10.1016/j.cma.2018.07.041
Colomés, O., G. Scovazzi, and J. Guilleminot. “On the robustness of variational multiscale error estimators for the forward propagation of uncertainty.” Computer Methods in Applied Mechanics and Engineering 342 (December 1, 2018): 384–413. https://doi.org/10.1016/j.cma.2018.07.041.
Colomés O, Scovazzi G, Guilleminot J. On the robustness of variational multiscale error estimators for the forward propagation of uncertainty. Computer Methods in Applied Mechanics and Engineering. 2018 Dec 1;342:384–413.
Colomés, O., et al. “On the robustness of variational multiscale error estimators for the forward propagation of uncertainty.” Computer Methods in Applied Mechanics and Engineering, vol. 342, Dec. 2018, pp. 384–413. Scopus, doi:10.1016/j.cma.2018.07.041.
Colomés O, Scovazzi G, Guilleminot J. On the robustness of variational multiscale error estimators for the forward propagation of uncertainty. Computer Methods in Applied Mechanics and Engineering. 2018 Dec 1;342:384–413.
Journal cover image

Published In

Computer Methods in Applied Mechanics and Engineering

DOI

ISSN

0045-7825

Publication Date

December 1, 2018

Volume

342

Start / End Page

384 / 413

Related Subject Headings

  • Applied Mathematics
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 01 Mathematical Sciences