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

Citations

Publications citing this paper.
Showing 1-10 of 25 extracted citations

References

Publications referenced by this paper.
Showing 1-10 of 24 references

Optimal L1-rate of convergence for viscosity methods and monotone schemes to piecewise constant solutions with shocks

Z.-H. TENG, P.-W. ZHANG
SIAM J. Numer. Anal., • 1997

Optimal Error Estimates for Viscosity Methods and Monotone Schemes to a Riemann Problem, Peking University Research Report #39

Z.-H. TENG
Institute of Mathematics and Department of Mathematics, Peking, • 1993

Regularity for Nonlinear Hyperbolic Conservation Laws

R. A. DEVORE, B. J. LUCIER
PREPRINT • 1993

WINTHER, An error estimate for a finite difference scheme approximating a hyperbolic system of conservation laws

R. A. TVEITO
SIAM J. Numer. Anal., • 1993

TADMOR, The convergence rate of approximate solutions for nonlinear scalar conservation laws

E. H. NESSYAHU
SIAM J. Numer. Anal., • 1992

Local error estimates for discontinuous solutions of nonlinear hyperbolic equations

E. TADMOR
SIAM J. Numer. Anal., • 1991

LUCIER, High order regularity for conservation laws

B.J.R.A. DEVORE
Indiana Univ. Math. J., • 1990

Similar Papers

Loading similar papers…