The extended finite element method for boundary layer problems in biofilm growth

Bryan G. Smith, Benjamin L. Vaughan, David L. Chopp

Research output: Contribution to journalArticlepeer-review

24 Scopus citations


In this paper, we use the eXtended Finite Element Method, with customized enrichment functions determined by asymptotic analysis, to study boundary layer behavior in elliptic equations with discontinuous coefficients. In particular, we look at equations where the coefficients are discontinuous across a boundary internal to the domain. We also show how to implement this method for Dirichlet conditions at an interface. The method requires neither the mesh to conform to the internal boundary, nor the mesh to have additional refinement near the interface, making this an ideal method for moving interface type problems. We then apply this method to equations for linearized biofilm growth to study the effects of biofilm geometry on the availability of substrate and the effect of tip-splitting in biofilm growth.

Original languageEnglish (US)
Pages (from-to)35-56
Number of pages22
JournalCommunications in Applied Mathematics and Computational Science
Issue number1
StatePublished - Jan 1 2007


  • Elliptic equations
  • Extended finite element method
  • Helmholtz quation, biofilms
  • Level set method
  • X-FEM

ASJC Scopus subject areas

  • Computer Science Applications
  • Computational Theory and Mathematics
  • Applied Mathematics


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