Error control for molecular statics problems

Serge Prudhomme*, Paul T. Bauman, J. Tinsley Oden

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

56 Scopus citations

Abstract

In this paper, we present an extension of goal-oriented error estimation and adaptation to the simulation of multiscale problems of molecular statics. Computable error estimates for the quasicontinuum method are developed with respect to specific quantities of interest, and an adaptive strategy based on these estimates is proposed for error control. The theoretical results are illustrated on a nanoindentation problem in which the quantity of interest is the force acting on the indenter. The promising capability of such error estimates and adaptive procedure for the solution of multiscale problems is demonstrated on numerical examples.

Original languageEnglish (US)
Pages (from-to)647-662
Number of pages16
JournalInternational Journal for Multiscale Computational Engineering
Volume4
Issue number5-6
DOIs
StatePublished - Dec 1 2006

Keywords

  • Error estimation
  • Goal-oriented adaptive modeling
  • Molecular statics
  • Multiscale problems
  • Quasicontinuum method

ASJC Scopus subject areas

  • Computational Mechanics
  • Computer Networks and Communications
  • Control and Systems Engineering

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