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

Benoît Merlet (1) , Julien Vovelle (2)

1 LAGA - Laboratoire Analyse, Géométrie et Applications
2 ICJ - Institut Camille Jordan

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]

Benoît Merlet, Julien Vovelle. Error estimate for the Finite Volume Scheme applied to the advection equation. Numerische Mathematik, 2007, 106 (1), pp.129--155. ⟨hal-00008660v2⟩