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 coeficients. In particular, we look at equations where the coeficients 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

Primary: 65N30, 92B05

Authors