Finite element methods of an operator splitting applied to population balance equations
type: Item
instance of: scholarly article
title: Finite element methods of an operator splitting applied to population balance equations
zbMATH Open document ID: 1242.65199
author: Naveed Ahmed
author: Gunar Matthies
author: Lutz Tobiska
published in: Journal of Computational and Applied Mathematics
publication date: 2011-12-21T00:00:00Z
review text: In population balance equations, the distribution of the entities depends not only on space and time but also on their own properties. The operator splitting method is used to transform the 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. The authors 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 main result is the unconditional stability of the method and derivation of optimal error estimates. Numerical tests are used to confirm the theoretical results.
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 35K20
zbMATH DE Number: 5991222
zbMATH Keywords: operator splitting
zbMATH Keywords: stabilized finite elements
zbMATH Keywords: population balance equations
zbMATH Keywords: numerical examples
zbMATH Keywords: discontinuous Galerkin method
zbMATH Keywords: time-dependent convection-diffusion problem
zbMATH Keywords: transient transport problem
zbMATH Keywords: backward Euler method
zbMATH Keywords: projection method
zbMATH Keywords: error estimates
zbMATH Keywords: stability
describes a project that uses: MooNMD
MaRDI profile type: Publication
full work available at URL: j.cam.2011.09.025
OpenAlex ID: W2042316664
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DOI: 10.1016/J.CAM.2011.09.025
description: scientific article; zbMATH DE number 5991222