Free Access
Issue
ESAIM: M2AN
Volume 47, Number 2, March-April 2013
Page(s) 609 - 633
DOI https://doi.org/10.1051/m2an/2012042
Published online 15 January 2013
  1. D. Aregba-Driollet and R. Natalini, Convergence of relaxation schemes for conservation laws. Appl. Anal. 1-2 (1996) 163–193. [CrossRef] [MathSciNet] [Google Scholar]
  2. D. Aregba-Driollet and R. Natalini, Discrete kinetic schemes for multidimensional systems of conservation laws. SIAM J. Numer. Anal. 37 (2000) 1973–2004. [CrossRef] [MathSciNet] [Google Scholar]
  3. S. Bianchini, B. Hanouzet and R. Natalini, Asymptotic behavior of smooth solutions for partially dissipative hyperbolic systems with a convex entropy. Commun. Pure Appl. Math. 60 (2007) 1559–1622. [CrossRef] [MathSciNet] [Google Scholar]
  4. J.A. Carrillo, B. Yan, An Asymptotic Preserving Scheme for the Diffusive Limit of Kinetic systems for Chemotaxis. Preprint. [Google Scholar]
  5. A. Chalabi, Convergence of relaxation schemes for hyperbolic conservation laws with stiff source terms. Math. Comput. 68 (1999) 955–970. [CrossRef] [Google Scholar]
  6. G.Q. Chen, T.P. Liu and C.D. Levermore, Hyperbolic conservation laws with stiff relaxation terms and entropy. Commun. Pure Appl. Math. 47 (1994) 787–830. [CrossRef] [MathSciNet] [Google Scholar]
  7. P. Degond, J.-G. Liu and M-H Vignal, Analysis of an asymptotic preserving scheme for the Euler-Poisson system in the quasineutral limit. SIAM J. Numer. Anal. 46 (2008) 1298–1322. [CrossRef] [MathSciNet] [Google Scholar]
  8. S. Deng, Asymptotic Preserving Schemes for Semiconductor Boltzmann Equation in the Diffusive Regime. CiCp (2012). [Google Scholar]
  9. G. Dimarco and L. Pareschi, Exponential Runge-Kutta methods for stiff kinetic equations. To appear. SIAM J. Numer. Anal. 49 (2011) 2057–2077. [CrossRef] [MathSciNet] [Google Scholar]
  10. F. Filbet and S. Jin, A class of asymptotic preserving schemes for kinetic equations and related problems with stiff sources. J.Comput. Phys. 229 (2010). [CrossRef] [MathSciNet] [Google Scholar]
  11. F. Filbet and S. Jin, An asymptotic preserving scheme for the ES-BGK model for he Boltzmann equation. J. Sci. Comput. 46 (2011). [CrossRef] [Google Scholar]
  12. E. Gabetta, L. Pareschi and G. Toscani, Relaxation schemes for nonlinear kinetic equations. SIAM J. Numer. Anal. 34 (1997) 2168–2194 [CrossRef] [MathSciNet] [Google Scholar]
  13. F. Golse, S. Jin and C.D. Levermore, The Convergence of Numerical Transfer Schemes in Diffusive Regimes I : The Discrete-Ordinate Method. SIAM J. Numer. Anal. 36 (1999) 1333–1369. [CrossRef] [MathSciNet] [Google Scholar]
  14. L. Gosse and G. Toscani, Space localization and well-balanced schemes for discrete kinetic models in diffusive regimes. SIAM J. Numer. Anal. 41 (2003) 641–658 [CrossRef] [MathSciNet] [Google Scholar]
  15. S. Jin, L. Pareschi and G. Toscani, Diffusive Relaxation Schemes for Discrete-Velocity Kinetic Equations. SIAM J. Numer. Anal. 35 (1998) 2405–2439. [CrossRef] [MathSciNet] [Google Scholar]
  16. S. Jin, Efficient asymptotic-preserving (AP) schemes for some multiscale kinetic equations. SIAM J. Sci. Comput. 21 (1999) 441–454. [CrossRef] [MathSciNet] [Google Scholar]
  17. A. Kurganov and E. Tadmor, Stiff systems of hyperbolic conservation laws : convergence and error estimates. SIAM J. Math. Anal. 28 (1997) 1446–1456. [CrossRef] [MathSciNet] [Google Scholar]
  18. T.P. Liu, Hyperbolic conservation laws with relaxation. Commun. Math. Phys. 1 (1987) 153–175. [CrossRef] [MathSciNet] [Google Scholar]
  19. G. Naldi and L. Pareschi, Numerical schemes for hyperbolic systems of conservation laws with stiff diffusive relaxation. SIAM J. Numer. Anal. 37 (2000) 1246–1270. [CrossRef] [MathSciNet] [Google Scholar]
  20. R. Natalini, Convergence to equilibrium for the relaxation approximations of conservation laws. Commun. Pure Appl. Math. 8 (1996) 795–823. [CrossRef] [Google Scholar]
  21. E. Tadmor and T. Tang, Pointwise error estimates for scalar conservation laws with piecewise smooth solutions. SIAM J. Numer. Anal. 36 (1999) 1739–1758. [CrossRef] [MathSciNet] [Google Scholar]
  22. E. Tadmor and T. Tang, Pointwise error estimates for relaxation approximations to conservation laws. SIAM J. Math. Anal. 32 (2000) 870–886. [CrossRef] [MathSciNet] [Google Scholar]
  23. T. Tang and J. Wang, Convergence of MUSCL relaxing schemes to the relaxed schemes of conservation laws with stiff source terms. J. Sci. Comput. 15 (2000) 173–195. [CrossRef] [Google Scholar]

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