Modeling error and adaptivity in nonlinear continuum mechanics

J. Tinsley Oden, Serge Prudhomme*, Daniel C. Hammerand, Mieczyslaw S. Kuczma

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

37 Scopus citations


In this paper, computable global bounds on errors due to the use of various mathematical models of physical phenomena are derived. The procedure involves identifying a so-called fine model among a class of models of certain events and then using that model as a datum with respect to which coarser models can be compared. The error inherent in a coarse model, compared to the fine datum, can be bounded by residual functionals unambiguously defined by solutions of the coarse model. Whenever there exist hierarchical classes of models in which levels of sophistication of various coarse models can be defined, an adaptive modeling strategy can be implemented to control modeling error. In the present work, the class of models is within those embodied in nonlinear continuum mechanics.

Original languageEnglish (US)
Pages (from-to)6663-6684
Number of pages22
JournalComputer Methods in Applied Mechanics and Engineering
Issue number49-50
StatePublished - Oct 12 2001
Externally publishedYes

Bibliographical note

Funding Information:
This work was supported by grant BF-2070 from Sandia National Laboratories and grant N0014-1-0124 from the Office of Naval Research. The subject of this paper appeared as Sandia Report SAND2001-0132 and a portion appeared as TICAM Report 00-24. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the US Department of Energy under Contract DE-AC04-94AL85000.

ASJC Scopus subject areas

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


Dive into the research topics of 'Modeling error and adaptivity in nonlinear continuum mechanics'. Together they form a unique fingerprint.

Cite this