Error estimate for the Finite Volume Scheme

Benoît Merlet (1, 2) , Julien Vovelle (3)

1 LAGA - Laboratoire Analyse, Géométrie et Applications
2 RAPSODI - Reliable numerical approximations of dissipative systems
3 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

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; error estimate; advection equation; Finite Volume method

Domaines: Equations aux dérivées partielles [math.AP]

Benoît Merlet, Julien Vovelle. Error estimate for the Finite Volume Scheme. Numerische Mathematik, 2007, 106 (1), pp.129-155. ⟨10.1007/s00211-006-0053-y⟩. ⟨hal-00008660v3⟩