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. (C) 2013 IMACS. Published by Elsevier B.V. All rights reserved.