Vol. 2, No. 1, 2007

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ISSN: 2157-5452 (e-only)
ISSN: 1559-3940 (print)
The extended finite element method for boundary layer problems in biofilm growth

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

Vol. 2 (2007), No. 1, 35–56
Abstract

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.

Keywords
X-FEM, extended finite element method, level set method, elliptic equations, Helmholtz equation, biofilms
Mathematical Subject Classification 2000
Primary: 65N30, 92B05
Milestones
Received: 8 July 2006
Accepted: 1 April 2007
Published: 2 August 2007
Authors
Bryan G. Smith
ESAM Department
Northwestern University
2145 Sheridan Road
Evanston, IL 60208
United States
Benjamin L. Vaughan Jr.
ESAM Department
Northwestern University
2145 Sheridan Road
Evanston, IL 60208
United States
David L. Chopp
ESAM Department
Northwestern University
2145 Sheridan Road
Evanston, IL 60208
United States