Goal-oriented error estimation for Cahn-Hilliard models of binary phase transition

Kristoffer G. Van Der Zee, J. Tinsley Oden, Serge Prudhomme, Andrea Hawkins-Daarud

Research output: Contribution to journalArticlepeer-review

26 Scopus citations


A posteriori estimates of errors in quantities of interest are developed for the nonlinear system of evolution equations embodied in the Cahn-Hilliard model of binary phase transition. These involve the analysis of wellposedness of dual backward-in-time problems and the calculation of residuals. Mixed finite element approximations are developed and used to deliver numerical solutions of representative problems in one- and two-dimensional domains. Estimated errors are shown to be quite accurate in these numerical examples.

Original languageEnglish (US)
Pages (from-to)160-196
Number of pages37
JournalNumerical Methods for Partial Differential Equations
Issue number1
StatePublished - Jan 2011
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-04-23
Acknowledged KAUST grant number(s): US00003
Acknowledgements: Contract grant sponsor: DOE Multiscale Mathematics; contract grant number: DE-FG02-05ER25701Contract grant sponsor: KAUST; contract grant number: US00003
This publication acknowledges KAUST support, but has no KAUST affiliated authors.


  • Cahn-Hilliard
  • a posteriori error estimation
  • diffuse interface
  • dual Cahn-Hilliard
  • dual well-posedness
  • error-residual equivalence
  • goal-oriented error analysis
  • linearized adjoint
  • quantities of interest

ASJC Scopus subject areas

  • Computational Mathematics
  • Analysis
  • Applied Mathematics
  • Numerical Analysis


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