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

Authors:
Naveed Ahmed;Gunar Matthies;Lutz Tobiska
Affiliations:
Universität Kassel, Fachbereich 10 Mathematik und Naturwissenschaften, Institut für Mathematik, Heinrich-Plett-Straíe 40, 34132 Kassel, Germany and Department of Mathematics, Kohat ...;Universität Kassel, Fachbereich 10 Mathematik und Naturwissenschaften, Institut für Mathematik, Heinrich-Plett-Straíe 40, 34132 Kassel, Germany;Institut für Analysis und Numerik, Otto-von-Guericke-Universität Magdeburg, Postfach 4120, D-39016 Magdeburg, Germany
Venue:
Applied Numerical Mathematics
Year:
2013

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Abstract

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.