An l1-error bound for a semi-implicit difference scheme applied to a stiff system of conservation laws

SIAM Journal on Numerical Analysis

Volumn 34, Issue 3, 1997, Pages 1152-1166

  Schroll, Hans Joachim ^a   Tveito, Aslak ^b   Winther, Ragnar ^b  

^a RWTH AACHEN UNIVERSITY   (Germany)

^b NONE

Author keywords

Error estimate; Non equilibrium; Relaxation term; Stiff hyperbolic conservation law

Indexed keywords

EID: 0039026206     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142994268855     Document Type: Article

References (19)

1. G. Q. CHEN AND T. P. LIU, Zero relaxation and dissipation limits for hyperbolic conservation laws, Comm. Pure Appl. Math., 46 (1993), pp. 755-781.
2. P. COLELLA, A. MAJDA, AND V. ROYTBURD, Theoretical and numerical structure for reacting shock waves, SIAM J. Sci. Statist. Comput., 7 (1986), pp. 1059-1080.
3. S. N. KRUZKOV, First order quasi linear equations with several space, variables, Math. USSR- Sb., 10 (1970), pp. 217-243.
4. N. N. KUZNETSOV, Accuracy of some approximate methods for computing the weak solutions of a first order quasi linear equation, U.S.S.R. Comput. Math, and Math. Phys., 16 (1976), pp. 105-119.
5. R. J. LEVEQUE AND J. WANG, A linear hyperbolic system with stiff source terms, in Notes on Numerical Fluid Mechanics, A. Donato and F. Oliver, eds., Vol. 43, Nonlinear Hyperbolic Problems: Theoretical, Applied and Computational Aspects, Viewog, 1992, pp. 401-408.
6. R. J. LEVEQUE AND H. C. YEE, A study of numerical methods for hyperbolic conservation laws with stiff source terms, J. Comput. Phys., 86 (1990), pp. 187-210.
7. A. LEVY, On Majda's model for dynamic combustion, Comm. Partial Differential Equations, 17 (1992), pp. 657-698.
8. T. P. Liu, Hyperbolic conservation laws with relaxation, Comm, Math. Phys., 108 (1987), pp. 153-175.
9. B. J. LUCIER, Error bounds for the methods of Glimm, Godunov and LeVeque, SIAM J. Numer. Anal., 22 (1985), pp. 1074-1081.
10. A. MAJDA, A qualitative model for dynamic combustion, SIAM J. Appl. Math., 41 (1981), pp. 70-93.
11. R. B. PEMBER, Numerical Methods for Hyperbolic Conservation Laws with Stiff Relaxation: I. Spurious Solutions, Center for Pure and Appl. Math., Univ. of California, Berkeley, CA, 1992, preprint.
12. R. B. PEMBER, Numerical methods for hyperbolic conservation laws with stiff relaxation: II. Higher-order Godunov methods, SIAM, J. Sci. Comput., 14 (1993), pp. 824-859.
13. H. K. RHEE, R. ARIS, AND N. R. AMUNDSEN, First-order Partial Differential Equations: Vol. I, Theory and Application of Hyperbolic Systems of Quasi Linear Equations, Prentice-Hall International series, Englewood, NJ, 1986.
14. H. K. RHEE, R. ARIS, AND N. R. AMUNDSEN, First-order Partial Differential Equations: Vol. II, Theory and Application of Hyperbolic Systems of Quasi Linear Equations, Prentice-Hall International series, Englewood, NJ, 1989.
15. B. SJöGREEN AND B. ENGQUIST, Numerical approximation of hyperbolic conservation laws with stiff terms, in Hyperbolic Problems, Theory, Numerical Methods and Applications, B. Egquist and B. Gustafsson, eds., Uppsala, 1991.
16. Z. TENG AND L. YING, Existence, uniqueness and convergence as vanishing viscosity for a reaction-diffusion-convection system, Acta Math. Sinica (N. S.), 5 (1989), pp. 114-135.
17. A. TVEITO AND R. WINTHER, On the rate of convergence to equilibrium for a system of conservation laws including a relaxation term, SIAM J. Math. Anal., 28 (1997), pp. 136-161.
18. A. TVEITO AND R. WINTHER, An error estimate for a finite difference scheme approximating a hyperbolic system of conservation laws. SIAM J. Numer. Anal., 30 (1993), pp. 401-424.
19. G. B. WHITHAM, Linear and Nonlinear Waves, John Wiley, New York, 1973.