Finite element methods of an operator splitting applied to population balance equations

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:236

Article

Ahmed, Naveed¹  Matthies, Gunar²  Tobiska, Lutz¹ 

[1] Univ Magdeburg, Inst Anal & Numer, D-39016 Magdeburg, Germany

[2] Univ Kassel, Fachbereich Math & Nat Wissensch 10, Inst Math, D-34132 Kassel, Germany

关键词: Operator splitting;    Discontinuous Galerkin;    Stabilized finite elements;    Population balance equations;   

DOI  :  10.1016/j.cam.2011.09.025

来源: Elsevier

【 摘 要 】

In population balance equations, the distribution of the entities depends not only on space and time but also on their own properties referred to as internal coordinates. The operator splitting method is used to transform the whole time-dependent problem into two unsteady subproblems of a smaller complexity. The first subproblem is a time-dependent convection-diffusion problem while the second one is a transient transport problem with pure advection. We use the backward Euler method to discretize the subproblems in time. Since the first problem is convection-dominated, the local projection method is applied as stabilization in space. The transport problem in the one-dimensional internal coordinate is solved by a discontinuous Galerkin method. The unconditional stability of the method will be presented. Optimal error estimates are given. Numerical tests confirm the theoretical results. (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

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