Estimation of modeling error in computational mechanics

J. Tinsley Oden*, Serge Prudhomme

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

145 Scopus citations

Abstract

We review and extend the theory and methodology of a posteriori error estimation and adaptivity for modeling error for certain classes of problems in linear and nonlinear mechanics. The basic idea is that for a given collection of physical phenomena a rich class of mathematical models can be identified, including models that are sufficiently refined and validated that they satisfactorily capture the events of interest. These fine models may be intractable, too complex to solve by existing means. Coarser models are therefore used. Moreover, as is frequently the case in applications, there are specific quantities of interest that are sought which are functionals of the solution of the fine model. In this paper, techniques for estimating modeling errors in such quantities of interest are developed. Applications to solid and fluid mechanics are presented.

Original languageEnglish (US)
Pages (from-to)496-515
Number of pages20
JournalJournal of Computational Physics
Volume182
Issue number2
DOIs
StatePublished - Nov 1 2002

Keywords

  • A posteriori modeling error estimation
  • Goal-oriented methods
  • Hierarchical modeling
  • Nonlinear continuum mechanics

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

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