Theory and methodology for estimation and control of errors due to modeling, approximation, and uncertainty

J. Tinsley Oden*, Ivo Babuška, Fabio Nobile, Yusheng Feng, Raul Tempone

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

55 Scopus citations


The reliability of computer predictions of physical events depends on several factors: the mathematical model of the event, the numerical approximation of the model, and the random nature of data characterizing the model. This paper addresses the mathematical theories, algorithms, and results aimed at estimating and controlling modeling error, numerical approximation error, and error due to randomness in material coefficients and loads. A posteriori error estimates are derived and applications to problems in solid mechanics are presented.

Original languageEnglish (US)
Pages (from-to)195-204
Number of pages10
JournalComputer Methods in Applied Mechanics and Engineering
Issue number2-5 SPEC. ISS.
StatePublished - Feb 4 2005
Externally publishedYes

Bibliographical note

Funding Information:
This work has been supported by an ITR grant 0205181 from National Science Foundation and by grant N00014-95-0401 from the Office of Naval Research. The calculation presented were done by Drs. Fabio Nobile and Yusheng Feng who implemented algorithm to estimate error due to uncertainty based on software developed by Dr. Leszek Demkowicz. Drs. Nobile’s and Tempone’s work was supported by an ICES Post Doctoral Fellowship Program. The adaptive quadrature algorithm used to compute bound in (5.3c) on uncertainty error was developed and implemented by Drs. Nobile and Tempone. The bounds used on the variances in the coefficients were the result of experimental tests performed by Dr. Kenneth Liechti and P. Hosatte. Drs. Leszek Demkowicz, and James C. Browne provided valuable advice during the course of this work.


  • Adaptive modeling
  • Modeling error estimation
  • Stochastic partial differential equations

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • General Physics and Astronomy
  • Computer Science Applications


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