On the convergence of operator splitting applied to conservation laws with source terms

SIAM Journal on Numerical Analysis

Volumn 33, Issue 3, 1996, Pages 843-863

  Langseth, J O ^a   Tveito, A ^b   Winther, R ^a  

^a UNIVERSITY OF OSLO   (Norway)

^b SINTEF   (Norway)

Author keywords

Error estimate; Hyperbolic conservation laws; Operator splitting

Indexed keywords

EID: 0000078308     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/0733042     Document Type: Article

References (20)

1. A. J. CHORIN, T. J. R. HUGHES, M. F. MCCRACKEN, AND J. E. MARSDEN, Product formulas and numerical algorithms, Comm. Pure Appl. Math., 31 (1978), pp. 200-256.
2. M. CRANDALL AND A. MAJDA, The method of fractional steps for conservation laws, Numer. Math., 34 (1980), pp. 285-314.
3. C. M. DAFERMOS, Polygonal approximations of solutions of the initial value problem for a conservation law, J. Math. Anal. Appl., 38 (1972), pp. 33-41.
4. G. W. HEDSTROM, Some numerical experiments with Dafermos' method for nonlinear hyperbolic equations, Lecture Notes in Math. 267, Springer-Verlag, Berlin, New York, 1972, pp. 117-138.
5. H. HOLDEN, L. HOLDEN, AND R. HØEOH-KROHN, A numerical method for first order nonlinear scalar conservation laws in one dimension, Comput. Math. Appl., 15 (1988), pp. 595-602.
6. H. HOLDEN AND N. H. RISEBRO, A method of fractional steps for scalar conservation laws without the CFL condition, Math. Comp., 60 (1993), pp. 221-232
7. _, Conservation laws with a random source, Preprint Series, Institute of Mathematics, University of Oslo, Norway, 1993.
8. J. KEVORKIAN, Partial Differential Equations, Analytical Solution Techniques, The Wadsworth & Brooks/Cole Mathematics Series, Pacific Grove, CA, 1990.
9. N. KRUZKOV, First order quasilinear equations with several space variables, Math. USSR-Sb., 10 (1970), pp. 217-243.
10. N. N. KUZNETSOV, Accuracy of some approximate methods for computing the weak solutions of a first order quasilinear equation, USSR Comp. Math Math Phys, 16 (1976), pp. 105-119.
11. R. J. LEVEQUE AND H. Y. YEE, A study of numerical methods for hyperbolic conservation laws with stiff source terms, J. Comp. Phys., 86 (1990), pp. 187-210.
12. J. O. LANGSETH, N. H. RISEBRO, AND A. TVEITO, A conservative front tracking scheme for 1D hyperbolic conservation laws, Proceedings from the Fourth International Conference on Hyperbolic Problems, Donato, Oliveri, eds., Taormina-Italy, 1992.
13. B. J. LUCIER, A moving mesh numerical method for hyperbolic conservation laws, Math. Comp., 46 (1986), pp. 59-69.
14. _, Error bounds for the methods of Glimm, Godunov and LeVeque, SIAM J. Numer. Anal., 22 (1985), pp. 1074-1081.
15. O. OLEINIK, Discontinuous solutions of nonlinear differential equations, Amer. Math. Soc. Transl. Ser. 2, 26 (1963), pp. 95-172.
16. N. H. RISEBRO, A front tracking alternative to the Random Choice Method, Proc. Amer. Math. Soc., 117 (1993), pp. 1125-1139.
17. N. H. RISEBRO AND A. TVEITO, Front tracking applied to a nonstrictly hyperbolic system of conservation laws, SIAM J. Sci. Statist. Comput., 12 (1991), pp. 1401-1419.
18. _, A front tracking method for conservation laws in one dimension, J. Comp. Phys., 101 (1992), pp. 130-139.
19. Z-H TENG, On the accuracy of fractional step methods for conservation laws in two dimensions, SIAM J. Numer. Anal., 31 (1994), pp. 43-63.
20. H. WESTERBERGER AND J. BALLMANN, The homogeneous homoentropic compression or expansion - A test case for analyzing Sod's operator-splitting, in Notes on Numerical Fluid Mechanics 24, J. Ballmann and R. Jeltsch, eds., 1988.