Stabilized finite element discretization applied to an operator-splitting method of population balance equations

An operator-splitting method is applied to transform the population balance equation into two subproblems: a transient transport problem with pure advection and a time-dependent convection–diffusion problem. For discretizing the two subproblems the discontinuous Galerkin method and the streamline upwind Petrov–Galerkin method combined with a backward Euler scheme in time are considered. Standard energy arguments lead to error estimates with a lower bound on the time step length. The stabilization vanishes in the time-continuous limit case. For this reason, we follow a new technique proposed by John and Novo for transient convection–diffusion–reaction equations and extend it to the case of population balance equations. We also compare numerically the streamline upwind Petrov–Galerkin method and the local projection stabilization method.