Duality-based adaptivity in finite element discretization of heterogeneous multiscale problems

Matthias Maier, Rolf Rannacher

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


This paper introduces an framework for adaptivity for a class of heterogeneous multiscale finite element methods for elliptic problems, which is suitable for a posteriori error estimation with separated quantification of the model error as well as the macroscopic and microscopic discretization errors. The method is derived within a general framework for 'goal-oriented' adaptivity, the so-called Dual Weighted Residual (DWR) method. This allows for a systematic a posteriori balancing of multiscale modeling and discretization. The developed method is tested numerically at elliptic diffusion problems for different types of heterogeneous oscillatory coefficients.

Original languageEnglish (US)
Pages (from-to)167-187
Number of pages21
JournalJournal of Numerical Mathematics
Issue number3
StatePublished - Oct 1 2016

Bibliographical note

Publisher Copyright:
© 2016 Walter de Gruyter GmbH, Berlin/Boston.


  • DWR method
  • Heterogeneous multiscale method
  • finite element method
  • goal-oriented adaptivity
  • mesh adaptation
  • model adaptation


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