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Convergence of a finite volume scheme for coagulation-fragmentation equations


Authors: Jean-Pierre Bourgade and Francis Filbet
Journal: Math. Comp. 77 (2008), 851-882
MSC (2000): Primary 65R20, 82C05
DOI: https://doi.org/10.1090/S0025-5718-07-02054-6
Published electronically: December 13, 2007
MathSciNet review: 2373183
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Abstract: This paper is devoted to the analysis of a numerical scheme for the coagulation and fragmentation equation. A time explicit finite volume scheme is developed, based on a conservative formulation of the equation. It is shown to converge under a stability condition on the time step, while a first order rate of convergence is established and an explicit error estimate is given. Finally, several numerical simulations are performed to investigate the gelation phenomenon and the long time behavior of the solution.


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Additional Information

Jean-Pierre Bourgade
Affiliation: Institut de Mathématiques de Toulouse, Université Toulouse III, 118, route de Narbonne 31062 Toulouse cedex 09, France
Email: bourgade@mip.ups-tlse.fr

Francis Filbet
Affiliation: Université Lyon, Université Lyon 1, CNRS, UMR 5208 - Institut Camille Jordan, 43 Boulevard du 11 Novembre 1918, F-69622 Villeurbanne cedex, France
Email: filbet@math.univ-lyon1.fr

DOI: https://doi.org/10.1090/S0025-5718-07-02054-6
Keywords: Coagulation-fragmentation equation, finite volume method
Received by editor(s): March 8, 2006
Received by editor(s) in revised form: October 31, 2006, January 3, 2007, and March 1, 2007
Published electronically: December 13, 2007
Additional Notes: The second author was supported in part by ANR Grant MNEC
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.