High-order semi-discrete central-upwind schemes for multi-dimensional Hamilton-Jacobi equations

Journal of Computational Physics

Volumn 189, Issue 1, 2003, Pages 63-87

  Bryson, Steve ^a   Levy, Doron ^b  

^a NASA AMES RESEARCH CENTER   (United States)

^b STANFORD UNIVERSITY   (United States)

Author keywords

Central schemes; CWENO; Hamilton Jacobi equations; High order; Monotone fluxes; Semi disrete schemes; WENO

Indexed keywords

CENTRAL SCHEME; CENTRAL-UPWIND SCHEME; CWENO; HAMILTON - JACOBI EQUATIONS; HIGH-ORDER; HIGHER-ORDER; MONOTONE FLUXES; MULTI DIMENSIONAL; SEMI-DISRETE SCHEME; WENO;

STABILITY;

EID: 0038792198     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0021-9991(03)00201-8     Document Type: Article

References (30)

1. R. Abgrall, Numerical discretization of the first-order Hamilton-Jacobi equation on triangular meshes, Commun. Pure Appl. Math. 49 (1996) 1339-1373.
2. F. Bianco, G. Puppo, G. Russo, High order central schemes for hyperbolic systems of conservation laws, SIAM J. Sci. Comput. 21 (1999) 294-322.
3. S. Bryson, D. Levy, Central schemes for multi-dimensional Hamilton-Jacobi equations, NAS Technical Report NAS-01-014, 2001, SIAM J. Sci. Comput. (to appear).
4. S. Bryson, D. Levy, High-order central WENO schemes for 1D Hamilton-Jacobi equations, Proc. Enumath 2001, Ischia, Italy (to appear).
5. S. Bryson, D. Levy, High-order central WENO schemes for multi-dimensional Hamilton-Jacobi equations, NAS Technical Report NAS-02-004, SIAM J. Numer. Anal. (to appear).
6. M.G. Crandall, H. Ishii, P.-L. Lions, User's guide to viscosity solutions of second order partial differential equations, Bull. Am. Math. Soc. 27 (1992) 1-67.
7. M.G. Crandall, P.-L. Lions, Viscosity solutions of Hamilton-Jacobi equations, Trans. Am. Math. Soc. 277 (1983) 1-42.
8. K.O. Friedrichs, P.D. Lax, Systems of conservation equations with a convex extension, Proc. Natl. Acad. Sci. 68 (1971) 1686-1688.
9. S. Gottlieb, C.-W. Shu, E. Tadmor, Strong stability-preserving high order time discretization methods, SIAM Rev. 43 (2001) 89-112.
10. A. Harten, B. Engquist, S. Osher, S. Chakravarthy, Uniformly high order accurate essentially non-oscillatory schemes III, J. Comput. Phys. 71 (1987) 231-303.
11. G.-S. Jiang, D. Peng, Weighted ENO schemes for Hamilton-Jacobi equations, SIAM J. Sci. Comput. 21 (2000) 2126-2143.
12. G.-S. Jiang, C.-W. Shu, Efficient implementation of weighted ENO schemes, J. Comput. Phys. 126 (1996) 202-228.
13. S. Jin, Z. Xin, Numerical passage from systems of conservation laws to Hamilton-Jacobi equations and relaxation schemes, SIAM J. Numer. Anal. 35 (1998) 2385-2404.
14. A. Kurganov, D. Levy, A third-order semi-discrete scheme for conservation laws and convection-diffusion equations, SIAM J. Sci. Comput. 22 (2000) 1461-1488.
15. A. Kurganov, S. Noelle, G. Petrova, Semi-discrete central-upwind schemes for hyperbolic conservation laws and Hamilton-Jacobi equations, SIAM J. Sci. Comput. 23 (2001) 707-740.
16. A. Kurganov, E. Tadmor, New high-resolution semi-discrete central schemes for Hamilton-Jacobi equations, J. Comput. Phys. 160 (2000) 720-742.
17. A. Kurganov, E. Tadmor, New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations, J. Comput. Phys. 160 (2000) 241-282.
18. D. Levy, G. Puppo, G. Russo, A fourth order central WENO scheme for multi-dimensional hyperbolic systems of conservation laws, SIAM J. Sci. Comput. 24 (2002) 480-506.
19. D. Levy, G. Puppo, G. Russo, Central WENO schemes for hyperbolic systems of conservation laws, Math. Model. Numer. Anal. 33 (3) (1999) 547-571.
20. D. Levy, G. Puppo, G. Russo, Compact central WENO schemes for multidimensional conservation laws, SIAM J. Sci. Comput. 22 (2000) 656-672.
21. P.L. Lions, Generalized Solutions of Hamilton-Jacobi Equations, Pitman, London, 1982.
22. P.L. Lions, P.E. Souganidis, Convergence of MUSCL and filtered schemes for scalar conservation laws and Hamilton-Jacobi equations, Numer. Math. 69 (1995) 441-470.
23. 1-stability and error estimates for approximate Hamilton-Jacobi solutions, Numer. Math. 87 (2001) 701-735.
24. C.-T. Lin, E. Tadmor, High-resolution non-oscillatory central schemes for approximate Hamilton-Jacobi equations, SIAM J. Sci. Comput. 21 (6) (2000) 2163-2186.
25. X.-D. Liu, S. Osher, T. Chan, Weighted essentially non-oscillatory schemes, J. Comput. Phys. 115 (1994) 200-212.
26. H. Nessyahu, E. Tadmor, Non-oscillatory central differencing for hyperbolic conservation laws, J. Comput. Phys. 87 (2) (1990) 408-463.
27. S. Osher, J. Sethian, Fronts propagating with curvature dependent speed: algorithms based on Hamilton-Jacobi formulations, J. Comput. Phys. 79 (1988) 12-49.
28. S. Osher, C.-W. Shu, High-order essentially nonoscillatory schemes for Hamilton-Jacobi equations, SIAM J. Numer. Anal. 28 (1991) 907-922.
29. P.E. Souganidis, Approximation schemes for viscosity solutions of Hamilton-Jacobi equations, J. Diff. Equations 59 (1985) 1-43.
30. Y.-T. Zhang, C.-W. Shu, High-order WENO schemes for Hamilton-Jacobi equations on triangular meshes, NASA/CR-2001-211256, ICASE Report No. 2001-39, SIAM J. Sci. Comput., 2001 (to appear).