Characteristic finite element analysis of pattern formation dynamical model in polymerizing actin flocks.

To illustrate the characteristic states of actin wave formation numerically, such as, spots, spirals and traveling waves, we propose a finite element method for simulating pattern formation in polymerizing actin flocks. Here we use the traditional Galerkin finite element method to solve the average filament polarization equation, and a mass-conservative characteristic finite element method to solve the density of actin equation, which deals well with the convection-dominated problem and keeps the mass balance globally. We study the convergence of this method and give the corresponding error estimate under some regularity assumptions of the solution. Finally some numerical results show the pattern formation in polymerizing actin flocks.