### Convergence Rates for Relaxation Schemes Approximating Conservation Laws

H.L. Liu and G. Warnecke

Abstract: In this paper, we prove a global error estimate for a relaxation scheme approximating scalar conservation laws. To this end, we decompose the error into a relaxation error and a discretization error. Including an initial error $\omega(\ep)$ we obtain the rate of convergence of $\sqrt{\ep}$ in $L^1$ for the relaxation step. The estimate here is independent of the type of nonlinearity. In the discretization step a convergence rate of $\sqrt{\Del x}$ in $L^1$ is obtained. These rates are independent of the choice of initial error $\omega(\ep)$. Thereby, we obtain the order $1/2$ for the total error.

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Author(s):
H.L. Liu, <hailiang.liu@mathematik.uni-magdeburg.de>
G. Warnecke, <gerald.warnecke@mathematik.uni-magdeburg.de>
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