Free Access
Issue
ESAIM: M2AN
Volume 41, Number 1, January-February 2007
Page(s) 169 - 185
DOI https://doi.org/10.1051/m2an:2007011
Published online 26 April 2007
  1. F. Bouchut, Nonlinear Stability of Finite Volume Methods for Hyperbolic Conservation Laws and Well-Balanced Schemes for Sources. Birkhäuser (2004). [Google Scholar]
  2. A. Bressan, H.K. Jenssen and P. Baiti, An instability of the Godunov Scheme. arXiv:math.AP/0502125 v2 (2005). [Google Scholar]
  3. M.J. Castro, J. Macías and C. Parés, A Q-Scheme for a class of systems of coupled conservation laws with source term. Application to a two-layer 1-D shallow water system. Math. Mod. Num. Anal. 35 (2001) 107–127. [CrossRef] [EDP Sciences] [Google Scholar]
  4. F. Coquel, D. Diehl, C. Merkle and C. Rohde, Sharp and diffuse interface methods for phase transition problems in liquid-vapour flows, in Numerical Methods for Hyperbolic and Kinetic Problems, IRMA Lectures in Mathematics and Theoretical Physics, Proceedings of CEMRACS 2003. [Google Scholar]
  5. 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]
  6. F. De Vuyst, Schémas non-conservatifs et schémas cinétiques pour la simulation numérique d'écoulements hypersoniques non visqueux en déséquilibre thermochimique. Ph.D. thesis, University of Paris VI, France (1994). [Google Scholar]
  7. E. Godlewski and P.A. Raviart, Numerical Approximation of Hyperbolic Systems of Conservation Laws. Springer (1996). [Google Scholar]
  8. L. Gosse, A well-balanced flux-vector splitting scheme designed for hyperbolic systems of conservation laws with source terms. Comput. Math. Appl. 39 (2000) 135–159. [CrossRef] [MathSciNet] [Google Scholar]
  9. 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]
  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. J.M. Greenberg, A.Y. LeRoux, R. Baraille and A. Noussair, Analysis and approximation of conservation laws with source terms. SIAM J. Numer. Anal. 34 (1997) 1980–2007. [CrossRef] [MathSciNet] [Google Scholar]
  12. A. Harten, P.D. Lax and B. Van Leer, On upstream differencing and Godunov-type schemes for hyperbolic conservation laws. SIAM Rev. 25 (1983) 35–61. [CrossRef] [MathSciNet] [Google Scholar]
  13. T. Hou and P.G. LeFloch, Why nonconservative schemes converge to wrong solutions: error analysis. Math. Comp. 62 (1994) 497–530. [CrossRef] [MathSciNet] [Google Scholar]
  14. 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]
  15. P.D. Lax and B. Wendroff, Systems of conservation laws. Comm. Pure Appl. Math. 13 (1960) 217–237. [CrossRef] [MathSciNet] [Google Scholar]
  16. P.G. LeFloch, Shock waves for nonlinear hyperbolic systems in nonconservative form. Institute Math. Appl., Minneapolis, Preprint 593 (1989). [Google Scholar]
  17. P.G. LeFloch, Graph solutions of nonlinear hyperbolic systems. J. Hyper. Differ. Equa. 2 (2004) 643–689. [Google Scholar]
  18. P.G. LeFloch and A.E. Tzavaras, Representation of weak limits and definition of nonconservative products. SIAM J. Math. Anal. 30 (1999) 1309–1342. [CrossRef] [MathSciNet] [Google Scholar]
  19. R.J. LeVeque, Balancing source terms and flux gradients in high-resolution Godunov methods: the quasi-steady wave-propagation algorithm. J. Comp. Phys. 146 (1998) 346–365. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  20. C. Parés, Numerical methods for nonconservative hyperbolic systems: a theoretical framework. SIAM J. Numer. Anal. 44 (2006) 300–321. [CrossRef] [MathSciNet] [Google Scholar]
  21. C. Parés and M. Castro, On the well-balance property of Roe's method for nonconservative hyperbolic systems. Applications to shallow water systems. Math. Mod. Num. Anal. 38 (2004) 821–852. [CrossRef] [EDP Sciences] [Google Scholar]
  22. A.I. Volpert, The space BV and quasilinear equations. Math. USSR Sbornik 73 (1967) 225–267. [CrossRef] [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