Convergence Rates for Relaxation Schemes Approximating Conservation Laws

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 L1 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 L1 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.