Free Access
Issue
ESAIM: M2AN
Volume 36, Number 3, May/June 2002
Page(s) 397 - 425
DOI https://doi.org/10.1051/m2an:2002019
Published online 15 August 2002
  1. A. Abdulle, Fourth Order Chebyshev Methods with Recurrence Relation. SIAM J. Sci. Comput. 23 (2002) 2041-2054. [CrossRef] [MathSciNet] [Google Scholar]
  2. A. Abdulle and A. Medovikov, Second Order Chebyshev Methods Based on Orthogonal Polynomials. Numer. Math. 90 (2001) 1-18. [CrossRef] [MathSciNet] [Google Scholar]
  3. P. Arminjon and M.-C. Viallon, Généralisation du schéma de Nessyahu-Tadmor pour une équation hyperbolique à deux dimensions d'espace. C. R. Acad. Sci. Paris Sér. I Math. t. 320 (1995) 85-88. [Google Scholar]
  4. P. Arminjon, M.-C. Viallon and A. Madrane, A Finite Volume Extension of the Lax-Friedrichs and Nessyahu-Tadmor Schemes for Conservation Laws on Unstructured Grids. Int. J. Comput. Fluid Dyn. 9 (1997) 1-22. [CrossRef] [MathSciNet] [Google Scholar]
  5. E. Audusse, M.O. Bristeau and B. Perthame, Kinetic Schemes for Saint-Venant Equations With Source Terms on Unstructured Grids. INRIA Report RR-3989 (2000). [Google Scholar]
  6. A. Bermudez and M.E. Vasquez, Upwind Methods for Hyperbolic Conservation Laws With Source Terms. Comput. & Fluids 23 (1994) 1049-1071. [CrossRef] [MathSciNet] [Google Scholar]
  7. F. Bianco, G. Puppo and G. Russo, High Order Central Schemes for Hyperbolic Systems of Conservation Laws. SIAM J. Sci. Comput. 21 (1999) 294-322. [CrossRef] [MathSciNet] [Google Scholar]
  8. T. Buffard, T. Gallouët and J.-M. Hérard, A Sequel to a Rough Godunov Scheme. Application to Real Gas Flows. Comput. & Fluids 29-7 (2000) 813-847. [CrossRef] [MathSciNet] [Google Scholar]
  9. S. Gottlieb, C.-W. Shu and E. Tadmor, High Order Time Discretization Methods with the Strong Stability Property. SIAM Rev. 43 (2001) 89-112. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  10. K.O. Friedrichs and P.D. Lax, Systems of Conservation Equations with a Convex Extension. Proc. Nat. Acad. Sci. USA 68 (1971) 1686-1688. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  11. T. Gallouët, J.-M. Hérard and N. Seguin, Some Approximate Godunov Schemes to Compute Shallow-Water Equations with Topography. Computers and Fluids (to appear). [Google Scholar]
  12. J.F. Gerbeau and B. Perthame, Derivation of Viscous Saint-Venant System for Laminar Shallow Water; Numerical Validation. Discrete Contin. Dynam. Systems Ser. B 1 (2001) 89-102. [Google Scholar]
  13. L. Gosse, A Well-Balanced Scheme Using Non-Conservative Products Designed for Hyperbolic Systems of Conservation Laws With Source Terms. Math. Models Methods Appl. Sci. 11 (2001) 339-365. [CrossRef] [MathSciNet] [Google Scholar]
  14. A. Harten, B. Engquist, S. Osher and S.R. Chakravarthy, Uniformly High Order Accurate Essentially Non-Oscillatory Schemes III. J. Comput. Phys. 71 (1987) 231-303. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  15. G.-S. Jiang and E. Tadmor, Nonoscillatory Central Schemes for Multidimensional Hyperbolic Conservation Laws. SIAM J. Sci. Comput. 19 (1998) 1892-1917. [CrossRef] [MathSciNet] [Google Scholar]
  16. S. Jin, A Steady-state Capturing Method for Hyperbolic System with Geometrical Source Terms. ESAIM: M2AN 35 (2001) 631-645. [CrossRef] [EDP Sciences] [Google Scholar]
  17. A. Kurganov and D. Levy, A Third-Order Semi-Discrete Scheme for Conservation Laws and Convection-Diffusion Equations. SIAM J. Sci. Comput. 22 (2000) 1461-1488. [CrossRef] [MathSciNet] [Google Scholar]
  18. A. Kurganov, S. Noelle and G. Petrova, Semi-Discrete Central-Upwind Schemes for Hyperbolic Conservation Laws and Hamilton-Jacobi Equations. SIAM J. Sci. Comput. 23 (2001) 707-740. [CrossRef] [MathSciNet] [Google Scholar]
  19. A. Kurganov and G. Petrova, A Third-Order Semi-Discrete Genuinely Multidimensional Central Scheme for Hyperbolic Conservation Laws and Related Problems. Numer. Math. 88 (2001) 683-729. [CrossRef] [MathSciNet] [Google Scholar]
  20. A. Kurganov and G. Petrova, Central Schemes and Contact Discontinuities. ESAIM: M2AN 34 (2000) 1259-1275. [CrossRef] [EDP Sciences] [Google Scholar]
  21. A. Kurganov and E. Tadmor, New High-Resolution Central Schemes for Nonlinear Conservation Laws and Convection-Diffusion Equations. J. Comput. Phys. 160 (2000) 214-282. [Google Scholar]
  22. B. van Leer, Towards the Ultimate Conservative Difference Scheme, V. A Second Order Sequel to Godunov's Method. J. Comput. Phys. 32 (1979) 101-136. [NASA ADS] [CrossRef] [Google Scholar]
  23. R.J. LeVeque, Balancing Source Terms and Flux Gradients in High-Resolution Godunov Methods: The Quasi-Steady Wave-Propagation Algorithm. J. Comput. Phys. 146 (1998) 346-365. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  24. R.J. LeVeque and D.S. Bale, Wave Propagation Methods for Conservation Laws with Source Terms, Hyperbolic Problems: Theory, Numerics, Applications, Vol. II, Zürich (1998). Birkhäuser, Basel, Internat. Ser. Numer. Math. 130 (1999) 609-618. [Google Scholar]
  25. D. Levy, G. Puppo and G. Russo, Central WENO Schemes for Hyperbolic Systems of Conservation Laws. ESAIM: M2AN 33 (1999) 547-571. [CrossRef] [EDP Sciences] [Google Scholar]
  26. D. Levy, G. Puppo and G. Russo, Compact Central WENO Schemes for Multidimensional Conservation Laws. SIAM J. Sci. Comput. 22 (2000) 656-672. [CrossRef] [MathSciNet] [Google Scholar]
  27. S.F. Liotta, V. Romano and G. Russo, Central Schemes for Systems of Balance Laws, Hyperbolic Problems: Theory, Numerics, Applications, Vol. II, Zürich (1998). Birkhäuser, Basel, Internat. Ser. Numer. Math. 130 (1999) 651-660. [Google Scholar]
  28. X.-D. Liu and S. Osher, Nonoscillatory High Order Accurate Self Similar Maximum Principle Satisfying Shock Capturing Schemes. I. SIAM J. Numer. Anal. 33 (1996) 760-779. [CrossRef] [MathSciNet] [Google Scholar]
  29. X.-D. Liu, S. Osher and T. Chan, Weighted Essentially Non-Oscillatory Schemes. J. Comput. Phys. 115 (1994) 200-212. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  30. X.-D. Liu and E. Tadmor, Third Order Nonoscillatory Central Scheme for Hyperbolic Conservation Laws. Numer. Math. 79 (1998) 397-425. [CrossRef] [MathSciNet] [Google Scholar]
  31. A. Medovikov, High Order Explicit Methods for Parabolic Equations. BIT 38 (1998) 372-390. [CrossRef] [MathSciNet] [Google Scholar]
  32. H. Nessyahu and E. Tadmor, Non-Oscillatory Central Differencing for Hyperbolic Conservation Laws. J. Comput. Phys. 87 (1990) 408-463. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  33. S. Noelle, A Comparison of Third and Second Order Accurate Finite Volume Schemes for the Two-Dimensional Compressible Euler Equations, Hyperbolic Problems: Theory, Numerics, Applications, Vol. I, Zürich (1998). Birkhäuser, Basel, Internat. Ser. Numer. Math. 129 (1999) 757-766. [Google Scholar]
  34. B. Perthame and C. Simeoni, A Kinetic Scheme for the Saint-Venant System with a Source Term. École Normale Supérieure, Report DMA-01-13. Calcolo 38 (2001) 201-301. [CrossRef] [MathSciNet] [Google Scholar]
  35. G. Russo, Central Schemes for Balance Laws, Proceedings of HYP2000. Magdeburg (to appear). [Google Scholar]
  36. A.J.C. de Saint-Venant, Théorie du mouvement non-permanent des eaux, avec application aux crues des rivières et à l'introduction des marées dans leur lit. C. R. Acad. Sci. Paris 73 (1871) 147-154. [Google Scholar]
  37. C.-W. Shu, Total-Variation-Diminishing Time Discretizations. SIAM J. Sci. Comput. 6 (1988) 1073-1084. [Google Scholar]
  38. C.-W. Shu and S. Osher, Efficient Implementation of Essentially Non-Oscillatory Shock-Capturing Schemes. J. Comput. Phys. 77 (1988) 439-471. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  39. P.K. Sweby, High Resolution Schemes Using Flux Limiters for Hyperbolic Conservation Laws. SIAM J. Numer. Anal. 21 (1984) 995-1011. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  40. E. Tadmor, Convenient Total Variation Diminishing Conditions for Nonlinear Difference Schemes. SIAM J. Numer. Anal. 25 (1988) 1002-1014. [CrossRef] [MathSciNet] [Google Scholar]

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