by Hailiang Liu and Gerald Warnecke.

**Series:** 1998-31, Preprints

- 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

**This paper was published in:**

SIAM J. Numer. Anal. 37, No. 4, S. 1316 - 1337, 2000