Finite element methods of an operator splitting applied to population balance equations |
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Authors: | Naveed Ahmed Gunar Matthies |
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Institution: | a Institut für Analysis und Numerik, Otto-von-Guericke-Universität Magdeburg, Postfach 4120, D-39016 Magdeburg, Germanyb Universität Kassel, Fachbereich 10 Mathematik und Naturwissenschaften, Institut für Mathematik, Heinrich-Plett-Straße 40, 34132 Kassel, Germany |
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Abstract: | 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. |
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Keywords: | 65M12 65M15 65M60 |
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