Convergence Rates for Relaxation Schemes Approximating Conservation Laws

Authors:
Hailiang Liu;Gerald Warnecke
Affiliations:
-;-
Venue:
SIAM Journal on Numerical Analysis
Year:
2000

Citing 0
Cited 6

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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 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.