Error estimate for the Finite Volume Scheme applied to the advection equation

Julien Vovelle (1) , Benoit Merlet (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 LAGA - Laboratoire Analyse, Géométrie et Applications

We 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.

Mots clés: scalar conservation laws; advection equation; Finite Volume method; error estimate

Domaines: Equations aux dérivées partielles [math.AP]

Julien Vovelle, Benoit Merlet. Error estimate for the Finite Volume Scheme applied to the advection equation. 2005. ⟨hal-00008660v1⟩