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arXiv:math/0509274 [math.AP]AbstractReferencesReviewsResources

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

Benoit Merlet, Julien Vovelle

Published 2005-09-13, updated 2006-06-12Version 2

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.

Comments: 24 pages
Categories: math.AP
Subjects: 35L65, 65M15
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