Characteristic galerkin schemes for scalar conservation laws in two and three space dimensions

SIAM Journal on Numerical Analysis

Volumn 34, Issue 2, 1997, Pages 779-796

  Lin, Peixiong ^a,b   Morton, K W ^a,b   Suli E ^a,b  

^a INSTITUTE OF GEOLOGY AND GEOPHYSICS   (China)

^b UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

Characteristic galerkin method; Corner effects; Multidimensional conservation laws; Riemann stieltjes integral; Transport collapse operator

Indexed keywords

EID: 0012664092     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142993259299     Document Type: Article

References (25)

1. Y. BREMER, Average multivalued solutions for scalar conservation laws, SIAM J. Numer. Anal., 21 (1984), pp. 1013-1037.
2. T. CHANG (T. ZHANG) AND L. HSIAO (L. XIAO), The Riemann Problem and Interaction of Waves in Gas Dynamics, in Pitman Monographs and Surveys in Pure and Applied Mathematics 41, Pitman, Boston, MA, 1989.
3. P. N. CHILDS AND K. W. MORTON, Characteristic Galerkin methods for scalar conservation laws in one dimension, SIAM J. Numer. Anal., 27 (1990), pp. 553-594.
4. M. CRANDALL AND A. MAJDA, The method of fractional steps for conservation laws, Numer. Math., 34 (1980), pp. 285-314.
5. B, ENGQUIST AND S. USHER, One-sided difference approximations for nonlinear conservation laws, Math. Comp., 36 (1981), pp. 321-352.
6. S. K. GODUNOV, Finite difference methods for numerical computations of discontinuous solutions of the equations of fluid dynamics, Mat. Sb., 47 (1959), pp. 271-295.
7. J. B. GOODMAN AND R. J. LEVEQUE, On the accuracy of stable schemes for scalar conservation laws, Math. Comp., 45 (1985), pp. 15-21.
8. C. KLINGENBERG, On the Riemann Problem for Scalar Conservation Laws in Two Space Dimensions, Sonderforschungsbereich 123, Stochastische Mathematische Modelle, Preprint Nr. 665, 1992.
9. R. J. LEVEQUE, A large time step generalization of Godunov's method for systems of conservation laws, SIAM J. Numer. Anal., 22 (1985), pp. 1051-1073.
10. R. J. LEVEQUE, High resolution finite volume methods on arbitrary grids via wave propagation, J. Comput. Phys., 78 (1988), pp. 36-63.
11. P. LIN, K. W. MORTON, AND E. SÜLI, Euler characteristic Galerkin scheme with recovery, RAIRO Modél. Math. Anal. Numér., 27 (1993), pp. 863-894.
12. P. LIN, K. W. MORTON, AND E. SÜLI, Characteristic Galerkin schemes for scalar conservation laws in two space dimensions I: Formulation, Computing Laboratory Numerical Analysis report 92/1, Oxford University, Oxford, UK, 1992.
13. K. W. MORTON, Shock capturing, fitting and recovery, in Proceedings of the Eighth International Conference on Numerical Methods in Fluid Dynamics, Lecture Notes in Physics, Vol. 170, E. Krause, ed., Springer-Verlag, Berlin, 1982, pp. 77-93.
14. K. W. MORTON, Characteristic Galerkin methods for hyperbolic problems, in Proc. on Numerical Methods in Fluid Mechanics, Gesellschaft füur Angewandte Mathematik und Machanik, Rome, M. Pandolfi and R. Riva, eds., Vieweg, Wiesbaden, 1983, pp. 243-250.
15. K. W. MORTON, Generalized Galerkin methods for hyperbolic problems, Comput. Methods Appl. Mech. Engrg., 52 (1985), pp. 847-871.
16. K. W. MORTON AND P. N. CHILDS, Characteristic Galerkin methods for hyperbolic systems, in Proc. Second Internat. Conf. on Hyperbolic problems, Aachen, March 1988, J. Ballman and R. Jeltsch, eds., Vieweg, Wiesbaden, 1989, pp. 435-455.
17. K. W. MORTON, A. PRIESTLEY, AND E. SÜLI, Stability of the Lagrange-Galerkin methods with non-exact integration, RAIRO Modél. Math. Anal. Numér., 22 (1988), pp. 625-653.
18. K. W. MORTON AND A. STOKES, Generalised Galerkin methods for hyperbolic problems, in Proc. Conf. Mathematics of Finite Elements and Applications IV, J. R. Whiteman, ed., Academic Press, New York, 1982, pp. 421-431.
19. K. W. MORTON AND P. K. SWEBY, A comparison of flux limited difference scheme and characteristic Galerkin methods for shock modelling, J. Comput. Phys., 73 (1987), pp. 203-230.
20. I. NATANSON. Theory of Functions of a Real Variable, Vol. 1, Ungar, New York, 1955.
21. P. L. ROE, A basis for upwind differencing of the two-dimensional unsteady Euler equations, in Numerical Methods for Fluid Dynamics II, K. W. Morton and M. J. Baines, eds., Oxford University Press, London, 1986.
22. G. STRANG, On the construction and comparison of difference schemes, SIAM J. Numer. Anal., 5 (1968), pp. 506-517.
23. B. VAN LEER, Computational Methods for Ideal Compressible Flow, Tech. report CR172180, NASA, Hampton, VA, 1983.
24. B. VAN LEER, Multidimensional explicit difference schemes for hyperbolic conservation laws, Institute for Computer Applications in Science and Engineering, Hampton, VA, 83-61.
25. T. ZHANG AND Y. ZHENG, Two-dimensional Riemann problem for a single conservation law, Trans. Amer. Math. Soc., 312 (1989), pp. 589-619.