Numerical analysis of the second-order characteristic FEM for nonlinear aerosol dynamic equations

Aerosol modeling is very important to study the behavior of aerosol dynamics in atmospheric environment. In this paper we consider the nonlinear aerosol dynamic equations on time and particle size, which involve the advection–condensation process and the nonlinear coagulation process. For solving accurately the multiple sharp log-normal aerosol distributions, we study and analyze the second order characteristic finite element method for the aerosol dynamic equations. We strictly prove that the developed method has second-order accuracy in time. The scheme improves the first-order accuracy in time comparing to the classical characteristic method. Numerical experiments for the multiple log-normal aerosol distributions are further given to confirm the theoretical results.