Flux evaluation in primal and dual boundary-coupled problems

E. H. Van Brummelen*, K. G. Van Der Zee, V. V. Garg, S. Prudhomme

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

33 Scopus citations


A crucial aspect in boundary-coupled problems, such as fluid-structure interaction, pertains to the evaluation of fluxes. In boundary-coupled problems, the flux evaluation appears implicitly in the formulation and consequently, improper flux evaluation can lead to instability. Finite-element approximations of primal and dual problems corresponding to improper formulations can therefore be nonconvergent or display suboptimal convergence rates. In this paper, we consider the main aspects of flux evaluation in finite-element approximations of boundary-coupled problems. Based on a model problem, we consider various formulations and illustrate the implications for corresponding primal and dual problems. In addition, we discuss the extension to free-boundary problems, fluid-structure interaction, and electro-osmosis applications.

Original languageEnglish (US)
Article number010904
JournalJournal of Applied Mechanics, Transactions ASME
Issue number1
StatePublished - 2012


  • dual problems
  • electro-osmosis
  • fluid-structure interaction
  • flux extraction
  • free-boundary problems
  • goal-oriented adaptivity

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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