Nonoscillatory high order accurate self-similar maximum principle satisfying shock capturing schemes I

SIAM Journal on Numerical Analysis

Volumn 33, Issue 2, 1996, Pages 760-779

  Liu, Xu Dong ^a   Osher, Stanley ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

High order; Hyperbolic conservation laws; Nonoscillatory; TVB

Indexed keywords

EID: 1542576022     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/0733038     Document Type: Article

References (19)

1. A. HARTEN, On a class of high resolution total-variation-stable finite-difference schemes, SIAM J. Numer. Anal., 21 (1984), pp. 1-23.
2. A. HARTEN, B. ENGQUIST, S. OSHER, AND S. CHAKRAVARTHY, Uniformly high order accurate essentially nonoscillatory schemes III, J. Comp. Phys., 71 (1987), pp. 231-303; also ICASE Report No. 86-22, ICASE, Hampton, VA, April 1986.
3. A. HARTEN, B. ENGQUIST, S. OSHER, AND S. CHAKRAVARTHY, Uniformly high order accurate essentially nonoscillatory schemes III, J. Comp. Phys., 71 (1987), pp. 231-303; also ICASE Report No. 86-22, ICASE, Hampton, VA, April 1986.
4. A. HARTEN AND S. OSHER, Uniformly high-order accurate nonoscillatory schemes I, SIAM J. Numer. Anal., 24 (1987), pp. 279-309.
5. S. OSHER, Convergence of generalized MUSCL schemes, SIAM J. Numer. Anal., 22 (1985), pp. 947-961.
6. S. OSHER AND E. TADMOR, On the convergence of difference approximations to scalar conservation laws, Math. Comp., 50 (1988), pp. 19-51.
7. C.-W. SHU AND S. OSHER, Efficient implementation of essentially non-oscillatory shock-capturing schemes, J. Comp. Phys., 77 (1988), pp. 439-471.
8. _, Efficient implementation of essentially non-oscillatory shock-capturing schemes, II, J. Comp. Phys., 83 (1989), pp. 32-78.
9. B. ENGQUIST AND S. OSHER, Stable and entropy satisfying approximations for transonic flow calculations, Math. Comp., 34 (1980), pp. 45-75.
10. A. HARTEN, S. OSHER, B. ENGQUIST, AND S. CHAKRAVARTHY, Some results on uniformly high order accurate essentially nonoscillatory schemes, Appl. Numer. Math., 2 (1986), pp. 347-377.
11. R. SANDERS, A third-order accurate variation nonexpansive difference schemes for single nonlinear conservation laws, Math. Comp., 51 (1988), pp. 535-558.
12. B. TONG, Uniformly High Order Accurate Strictly Non-Oscillatory Numerical Schemes for Hyperbolic Conservation Law, Ph.D. thesis, University of California, Los Angeles, 1992.
13. C.-W. SHU, TVB uniformly high-order schemes for conservation laws, Math. Comp., 49 (1987), pp. 105-121.
14. _, TVB boundary treatment for numerical solutions of conservation laws, Math. Comp., 49 (1987), pp. 123-134.
15. B. COCKBURN AND C.-W. SHU, TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws II: General framework, Math. Comp., 52 (1989), pp. 411-435.
16. B. COCKBURN, S.-Y. LIN, AND C.-W. SHU, TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws III: One-dimensional systems, J. Comp. Phys., 84 (1989), pp. 90-113.
17. S. N. KRUZKOV, First order quasilinear equations in several independent variables, Math. USSR Sbornik, 10 (1970), pp. 217-243.
18. A. ROGERSON AND E. MEIBURG, A numerical study of the convergence properties of ENO schemes, J. Sci. Comput., 5 (1990), pp. 151-167.
19. C.-W. SHU, Numerical experiments on the accuracy of ENO and modified ENO schemes, J. Sci. Comput., 5 (1990), pp. 127-149.