EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 42 / No 3 (May-June 2008) ESAIM: M2AN, 42 3 (2008) 425-442 References
Free Access
Issue
ESAIM: M2AN
Volume 42, Number 3, May-June 2008
Page(s) 425 - 442
DOI https://doi.org/10.1051/m2an:2008011
Published online 03 April 2008
  1. N. Andrianov and G. Warnecke, On the solution to the Riemann problem for the compressible duct flow. SIAM J. Appl. Math. 64 (2004) 878–901. [CrossRef] [MathSciNet] [Google Scholar]
  2. E. Audusse, F. Bouchut, M.-O. Bristeau, R. Klein and B. Perthame, A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows. SIAM J. Sci. Comp. 25 (2004) 2050–2065. [CrossRef] [Google Scholar]
  3. R. Botchorishvili and O. Pironneau, Finite volume schemes with equilibrium type discretization of source terms for scalar conservation laws. J. Comput. Phys. 187 (2003) 391–427. [CrossRef] [MathSciNet] [Google Scholar]
  4. R. Botchorishvili, B. Perthame and A. Vasseur, Equilibrium schemes for scalar conservation laws with stiff sources. Math. Comput. 72 (2003) 131–157. [Google Scholar]
  5. F. Bouchut, Nonlinear stability of finite volume methods for hyperbolic conservation laws, and well-balanced schemes for sources, Frontiers in Mathematics series. Birkhäuser (2004). [Google Scholar]
  6. R. Courant and K.O. Friedrichs, Supersonic Flow and Shock Waves. John Wiley, New York (1948). [Google Scholar]
  7. G. Dal Maso, P.G. LeFloch and F. Murat, Definition and weak stability of nonconservative products. J. Math. Pures Appl. 74 (1995) 483–548. [MathSciNet] [Google Scholar]
  8. P. Goatin and P.G. LeFloch, The Riemann problem for a class of resonant nonlinear systems of balance laws. Ann. Inst. H. Poincaré Anal. Non Linéaire 21 (2004) 881–902. [CrossRef] [MathSciNet] [Google Scholar]
  9. L. Gosse, A well-balanced flux-vector splitting scheme designed for hyperbolic systems of conservation laws with source terms. Comp. Math. Appl. 39 (2000) 135–159. [CrossRef] [MathSciNet] [Google Scholar]
  10. J.M. Greenberg and A.Y. Leroux, A well-balanced scheme for the numerical processing of source terms in hyperbolic equations. SIAM J. Numer. Anal. 33 (1996) 1–16. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  11. A. Harten, P.D. Lax, C.D. Levermore and W.J. Morokoff, Convex entropies and hyperbolicity for general Euler equations. SIAM J. Numer. Anal. 35 2117–2127 (1998). [Google Scholar]
  12. E. Isaacson and B. Temple, Nonlinear resonance in systems of conservation laws. SIAM J. Appl. Math. 52 (1992) 1260–1278. [CrossRef] [MathSciNet] [Google Scholar]
  13. E. Isaacson and B. Temple, Convergence of the 2 x 2 Godunov method for a general resonant nonlinear balance law. SIAM J. Appl. Math. 55 (1995) 625–640. [CrossRef] [MathSciNet] [Google Scholar]
  14. D. Kröner and M.D. Thanh, On the Model of Compressible Flows in a Nozzle: Mathematical Analysis and Numerical Methods, in Proc. 10th Intern. Conf. “Hyperbolic Problem: Theory, Numerics, and Applications”, Osaka (2004), Yokohama Publishers (2006) 117–124. [Google Scholar]
  15. D. Kröner and M.D. Thanh, Numerical solutions to compressible flows in a nozzle with variable cross-section. SIAM J. Numer. Anal. 43 (2006) 796–824. [Google Scholar]
  16. P.G. LeFloch, Entropy weak solutions to nonlinear hyperbolic systems under nonconservative form. Comm. Partial. Diff. Eq. 13 (1988) 669–727. [Google Scholar]
  17. P.G. LeFloch, Shock waves for nonlinear hyperbolic systems in nonconservative form. Preprint 593, Institute Math. Appl., Minneapolis (1989). [Google Scholar]
  18. P.G. LeFloch, Hyperbolic systems of conservation laws: The theory of classical and non-classical shock waves, Lectures in Mathematics. ETH Zürich, Birkäuser (2002). [Google Scholar]
  19. P.G. LeFloch, Graph solutions of nonlinear hyperbolic systems. J. Hyper. Diff. Equ. 1 (2004) 243–289. [Google Scholar]
  20. P.G. LeFloch and T.-P. Liu, Existence theory for nonlinear hyperbolic systems in nonconservative form. Forum Math. 5 (1993) 261–280. [CrossRef] [MathSciNet] [Google Scholar]
  21. P.G. LeFloch and M.D. Thanh, The Riemann problem for fluid flows in a nozzle with discontinuous cross-section. Comm. Math. Sci. 1 (2003) 763–797. [Google Scholar]
  22. P.G. LeFloch and M.D. Thanh, The Riemann problem for the shallow water equations with discontinuous topography. Comm. Math. Sci. 5 (2007) 865–885. [Google Scholar]
  23. D. Marchesin and P.J. Paes-Leme, A Riemann problem in gas dynamics with bifurcation. Hyperbolic partial differential equations III. Comput. Math. Appl. (Part A) 12 (1986) 433–455. [MathSciNet] [Google Scholar]
  24. E. Tadmor, Skew selfadjoint form for systems of conservation laws. J. Math. Anal. Appl. 103 (1984) 428–442. [Google Scholar]
  25. E. Tadmor, A minimum entropy principle in the gas dynamics equations. Appl. Numer. Math. 2 (1986) 211–219. [CrossRef] [MathSciNet] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you