Finite volume scheme for multiple fragmentation Equations

Abstract

In this paper we study a finite volume approximation for the conservative formulation of multiple fragmentation models. We investigate the convergence of the numerical solutions towards a weak solution of the continuous problem by considering locally bounded kernels. The proof is based on the Dunford-Pettis theorem by using the weak L1 compactness method. The analysis of the method allows us to prove the convergence of the discretized approximated solution towards a weak solution to the continuous problem in a weighted L1 space.