2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/102259We study the convergence of a Finite Volume scheme for the linear advection equation with a Lipschitz divergence-free speed in $\R^d$. We prove a $h^{1/2}$-error estimate in the $L^\infty(0,t;L^1)$-norm for $BV$ data. This result was expected from numerical experiments and is optimal.24 pagesAnalysis of PDEsMSC Number: 35L65, 65M15text