# Analysis of the upwind finite volume method for general initial and boundary value transport problems

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1 LATP - Laboratoire d-Analyse, Topologie, Probabilités

Abstract : This paper is devoted to the convergence analysis of the upwind finite volume scheme for the initial and boundary value problem associated to the linear transport equation in any dimension, on general unstructured meshes. We are particularly interested in the case where the initial and boundary data are in $L^\infty$ and the advection vector field $v$ has low regularity properties, namely $v\in L^10,T,W^{1,1}\O^d$, with suitable assumptions on its divergence. In this general framework, we prove uniform in time strong convergence in $L^p\O$ with \$p

Autor: Franck Boyer -

Fuente: https://hal.archives-ouvertes.fr/

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