Convergence of a finite volume scheme for coagulation-fragmentation equations

Jean-Pierre Bourgade (1) , Francis Filbet (1)

1 MIP - Mathématiques pour l'Industrie et la Physique

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.

Mots clés: coagulation-fragmentation equation; finite volume method

Domaines: Analyse numérique [math.NA]

Jean-Pierre Bourgade, Francis Filbet. Convergence of a finite volume scheme for coagulation-fragmentation equations. Mathematics of Computation, 2008, 77, pp.851--882. ⟨hal-00090606⟩