  This paper focuses on the study of the Filament Based Lamellipodium Model
(FBLM) and the corresponding Finite Element Method (FEM) from a numerical point
of view. We study fundamental numerical properties of the FEM and justify the
further use of the FBLM. We exhibit that the FEM satisfies a timestep stability
condition that is consistent with the nature of the problem. We propose a
particular strategy to automatically adapt the time step of the method. We show
that the FEM convergences with respect to the (two-dimensional) space
discretization in a series of characteristic and representative experiments. We
embed and couple the FBLM with a complex extracellular environment comprised of
chemical and haptic components and study their combined time evolution. Under
this prism, we study the sensitivity of the FBLM on several of its controlling
parameters and discuss their influence in the development of the model.
