Se p 20 05 Error estimate for the Finite Volume Scheme applied to the advection equation
نویسنده
چکیده
We study the convergence of the Finite Volume Scheme for the advection equation with a divergence free C1 speed in a domain without boundary. We show that the rate of the L∞(0, T ;L1)-error estimate is h1/2 for BV data. This result was expected from numerical experiment and is optimal. The proof is based on Kuznetsov’s method. This method has been introduced for non-linear hyperbolic equations but for the improvements presented in this paper, the linearity of the initial equation is crucial.
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