The Optimal Convergence Rate of Monotone Finite Difference Methods for Hyperbolic Conservation Laws∗

@inproceedings{SIAMJ1997TheOC,
title={The Optimal Convergence Rate of Monotone Finite Difference Methods for Hyperbolic Conservation Laws∗},
author={N SIAMJ.},
year={1997}
}

N SIAMJ.

Published 1997

We are interested in the rate of convergence in L1 of the approximate solution of a conservation law generated by a monotone finite difference scheme. Kuznetsov has proved that this rate is 1/2 [USSR Comput. Math. Math. Phys., 16 (1976), pp. 105–119 and Topics Numer. Anal. III, in Proc. Roy. Irish Acad. Conf., Dublin, 1976, pp. 183–197], and recently Teng and Zhang have proved this estimate to be sharp for a linear flux [SIAM J. Numer. Anal., 34 (1997), pp. 959–978]. We prove, by constructing… CONTINUE READING