  We describe in this work the numerical treatment of the Filament Based
Lamellipodium Model (FBLM). The model itself is a two-phase two-dimensional
continuum model, describing the dynamics of two interacting families of locally
parallel F-actin filaments. It includes, among others, the bending stiffness of
the filaments, adhesion to the substrate, and the cross-links connecting the
two families. The numerical method proposed is a Finite Element Method (FEM)
developed specifically for the needs of these problem. It is comprised of
composite Lagrange-Hermite two dimensional elements defined over two
dimensional space. We present some elements of the FEM and emphasise in the
numerical treatment of the more complex terms. We also present novel numerical
simulations and compare to in-vitro experiments of moving cells.
