A moving mesh numerical method for hyperbolic conservation laws

Mathematics of Computation

Volumn 46, Issue 173, 1986, Pages 59-69

  Lucier, Bradley J ^a  

^a PURDUE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001844855     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-1986-0815831-4     Document Type: Article

References (27)

1. M. Berger, Adaptive Mesh Refinement for Hyperbolic Partial Differential Equations. Stanford Computer Science Report STAN-CS-82-924 (dissertation).
2. J. H. Bolstad, An Adaptive Finite Difference Method for Hyperbolic Systems in One Space Dimension. Lawrence Berkeley Lab. LBL-13287 (STAN-CS-82-899) (dissertation).
3. C. DE BOOR, "Good approximation by splines with variable knots, " in Spline Functions and Approximation Theory (A. Meir and A. Sharma, eds.), ISNM, v. 21, Birkhäuscr-Verlag, Basel, 1973, pp. 57-72.
4. M. G. Crandall & A. Majda, "Monotone difference approximations for scalar conservation laws, " Math. Comp., v. 34, 1980, pp. 1-21.
5. C. M. Dafermos, "Polygonal approximations of solutions of the initial value problem for a conservation law, " J. Math. Anal. Appl., v. 38, 1972, pp. 33-41.
6. S. F. Davis & J. E. Flaherty, "An adaptive finite element method for initial-value problems for partial differential equations, " SIAMJ. Sei. Statist. Comput., v. 3, 1982, pp. 6-28.
7. T. Dupont, "Mesh modification for evolution equations, " Math. Comp., v. 39, 1982, pp. 85-107.
8. A. Harten, "High resolution schemes for hyperbolic conservation laws, " J. Comput. Phys., v. 49, 1983, pp. 357-393.
9. A. Harten & J. M. Hyman, "Self-adjusting grid methods for one-dimensional hyperbolic conservation laws, " J. Comput. Phys., v. 50, 1983, pp. 235-269.
10. A. Harten, J. M. Hyman & P. D. Lax, "On finite difference approximations and entropy conditions for shocks, " Comm. Pure Appl. Math., v. 29, 1976, pp. 297-322.
11. G. W. Hedstrom, "Some numerical experiments with Dafermos's method for nonlinear hyperbolic equations, " Lecture Notes in Math., vol. 267, Springer-Verlag, Berlin and New York, 1972, pp. 117-138.
12. G W. Hedstrom & G. H. Rodrigue, "Adaptive-grid methods for time-dependent partial differential equations, " in Multigrid Methods (W. Hackbusch and U. Trottenberg, eds.). Springer-Verlag, Berlin and New York, 1982, pp. 474-484.
13. B. M. Herbst, S. W. Schoombie & A. R. Mitchell, "Equidistributing principles in moving finite element methods, " J. Comput. Appl. Math., v. 9, 1983, pp. 377-489.
14. S. N. KruZkov, "First order quasilinear equations with several space variables, " Math. USSR Sb., v. 10, 1970, pp. 217-243.
15. N. N. Kuznetsov, "Accuracy of some approximate methods for computing the weak solutions of a first-order quasi-linear equation, " USSR Comput. Math, and Math. Phys., v. 16, no. 6, 1976, pp. 105-119.
16. P. D. Lax, Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves, SIAM Regional Conference Lectures in Applied Mathematics, no. 11, 1972.
17. R. LeVeque, "Large time step shock-capturing techniques for scalar conservation laws, " SIAM J. Numer. Anal., v. 19, 1982, pp. 1091-1109.
18. B. J. Lucier, "A stable adaptive numerical scheme for hyperbolic conservation laws, " SIAM J. Numer. Anal., v. 22, 1985, pp. 180-203.
19. B. J. Lucier, "Error bounds for the methods of Glimm, Godunov, and LeVeque, " SIAM J. Numer. Anal., Dec. 1985.
20. B. J. Lucier, "On nonlocal monotone difference methods for scalar conservation laws, " Math. Comp. (To appear.)
21. K. Miller, "Moving finite elements, part II, " SIAMJ. Numer. Anal., v. 18, 1981, pp. 1019-1057.
22. J. Öliger, "Approximate methods for atmospheric and océanographie circulation problems, " Lecture Notes in Physics, vol. 91 (R. Glowinski and J. Lions, eds.), Springer-Verlag, Berlin and New York, 1979, pp. 171-184.
23. S. Osher & S. CHAKRAVARTHY High Resolution Schemes and the Entropy Condition, ICASE Report 172218.
24. S. Osher & R. Sanders, "Numerical approximations to nonlinear conservation laws with locally varying time and space grids, " Math. Comp., v. 41, 1983, pp. 321-336.
25. J. R. Rice, The Approximation of Functions, Vol. 1, Addison-Wesley, Reading, Mass., 1964.
26. R. Sanders, "On convergence of monotone finite difference schemes with variable spatial differencing, " Math. Comp., v. 40, 1983, pp. 91-106.
27. R. Sanders, "The moving grid method for nonlinear hyperbolic conservation laws, " SIAM J. Numer. Anal., v. 22, 1985, pp. 713-728.