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.


Paper:
Available as PostScript.
Author(s):
H.L. Liu, mailto:hailiang.liu@mathematik.uni-magdeburg.de
G. Warnecke, mailto:gerald.warnecke@mathematik.uni-magdeburg.de
Publishing information:
Comments:
Submitted by:
mailto:hailiang.liu@mathematik.uni-magdeburg.de June 7 1999.


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