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

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

2005-09-13

arxiv.org/abs/math/0509274v2

Mathematics

Analysis of PDEs

24 pages

Scientific paper

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.

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