98-31
Convergence Rates for Relaxation Schemes Approximating Conservation Laws
by Hailiang Liu and Gerald Warnecke
Preprint series: 98-31, Preprints
The paper is published: SIAM J. Numer. Anal. 37, No. 4, S. 1316 - 1337, 2000
- MSC:
- 35L65 Conservation laws
- 65M06 Finite difference methods
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 $\omega(\epsilon)$ we obtain the rate of convergence of $(\max \{\ep, \omega(\epsilon)\})^{1/2}$ 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 $(\Delta x)^{1/2}$ in $L^1$ is obtained and is independent of the choice of initial error $\omega(\ep)$. Thereby, we obtain the order $1/2$ for the total error.
Keywords: relaxation scheme, relaxation model, convergence rate
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