Convergence of a difference scheme for conservation laws with a discontinuous flux

SIAM Journal on Numerical Analysis

Volumn 38, Issue 2, 2001, Pages 681-698

  Towers, John D ^a  

^a NONE   (United States)

Author keywords

Conservation laws; Difference approximations; Discontinuous coefficients

Indexed keywords

EID: 0034449655     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142999363668     Document Type: Article

References (16)

1. M.G. CRANDALL AND A. MAJDA, Monotone difference approximations for scalar conservation laws, Math. Comp., 34 (1980), pp. 1-21.
2. B. ENGQUIST AND S. OSHER, One sided difference approximations for nonlinear conservation laws, Math. Comp., 36 (1980), pp. 45-75.
3. S.K. GODUNOV, A finite difference method for the numerical computation of discontinuous solutions of the equations of fluid dynamics, Math. USSR Sb., 47 (1959), pp. 271-290.
4. A. HARTEN, On a class of high resolution total-variation-stable finite-difference schemes, SIAM J. Numer. Anal., 21 (1984), pp. 1-23.
5. A. HARTEN, J.M. HYMAN, AND P.D. LAX, On finite difference approximations and entropy conditions for shocks, Comm. Pure Appl. Math., 29 (1976), pp. 297-322.
6. R. A. KLAUSEN AND N.H. RISEBRO, Stability of conservation laws with discontinuous coefficients, J. Differential Equations, 157 (1999), pp. 41-60.
7. C. KLINGENBERG AND N.H. RISEBRO, Convex conservation laws with discontinuous coefficients. Existence, uniqueness, and asymptotic behavior, Comm. Partial Differential Equations, 20 (1995), pp. 1959-1990.
8. S.N. KRUZKOV, First order quasilinear equations in several independent variables, Math. USSR Sb., 10, (1970), pp. 217-243.
9. N.N. KUZNETSOV, Accuracy of some approximate methods for computing the weak solutions of a first-order quasilinear equation, USSR Comp. Math. and Math. Phys., 16 (1976), pp. 105-119.
10. P.D. LAX AND B. WENDROFF, Systems of conservation laws, Comm. Pure Appl. Math., 23 (1960), pp. 217-237.
11. R.J. LEVEQUE, Numerical Methods for Conservation Laws, Birkhauser Verlag, Boston, 1992.
12. L. LIN, J.B. TEMPLE, AND J. WANG, A comparison of convergence rates for Godunov's method and Glimm's method in resonant nonlinear systems of conservation laws, SIAM J. Numer. Anal., 32 (1995), pp. 824-840.
13. L. LONGWEI, B. TEMPLE, AND W. JINGHUA, Suppression of oscillations in Godunov's method for a resonant non-strictly hyperbolic system, SIAM J. Numer. Anal., 32 (1995), pp. 841-864.
14. S. J. OSHER, Riemann solvers, the entropy condition, and difference approximations, SIAM J. Numer. Anal., 21 (1984), pp. 217-235.
15. S. OSHER AND S. CHAKRAVARTHY, High resolution schemes and the entropy condition, SIAM J. Numer. Anal., 21 (1984), pp. 955-984.
16. 1-contractive semigroup, Comm. Pure Appl. Math., 24 (1971), pp. 125-132.