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

In this paper, we use the eXtended Finite Element Method (X-FEM), with customized enrichment functions determined by asymptotic analysis, to study boundary layer behavior in elliptic equations with discontinuous coecien ts. In particular, we look at equations where the coecien ts 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 renemen t near the interface, making this an ideal method for moving interface type problems. We then apply this method to equations for linearized biolm growth to study the eects of biolm geometry on the availability of substrate and the eect of tip-splitting in biolm growth.

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