Asymptotic behavior of a diffusive scheme solving the inviscid one-dimensional pressureless gases system

Conference object English OPEN
Boudin, Laurent; Mathiaud, Julien;
(2012)
  • Publisher: AIMS
  • Subject: [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] | [ MATH.MATH-NA ] Mathematics [math]/Numerical Analysis [math.NA]

In this work, we discuss some numerical properties of the viscous numerical scheme introduced in [Boudin, Mathiaud, NMPDE 2012] to solve the one-dimensional pressureless gases system, and study in particular, from a computational viewpoint, its asymptotic behavior when ... View more
  • References (17)
    17 references, page 1 of 2

    [1] F. Berthelin, P. Degond, M. Delitala, and M. Rascle. A model for the formation and evolution of traffic jams. Arch. Ration. Mech. Anal., 187(2):185-220, 2008.

    [2] C. Berthon, M. Breuss, and M.-O. Titeux. A relaxation scheme for the approximation of the pressureless Euler equations. Numer. Methods Partial Differential Equations, 22(2):484-505, 2006.

    [3] F. Bouchut. On zero pressure gas dynamics. In Advances in kinetic theory and computing, volume 22 of Ser. Adv. Math. Appl. Sci., pages 171-190. World Sci. Publ., River Edge, NJ, 1994.

    [4] F. Bouchut and F. James. One-dimensional transport equations with discontinuous coefficients. Nonlinear Anal., 32(7):891-933, 1998.

    [5] F. Bouchut and F. James. Duality solutions for pressureless gases, monotone scalar conservation laws, and uniqueness. Comm. Partial Differential Equations, 24(11-12):2173-2189, 1999.

    [6] F. Bouchut, S. Jin, and X. Li. Numerical approximations of pressureless and isothermal gas dynamics. SIAM J. Numer. Anal., 41(1):135-158 (electronic), 2003.

    [7] L. Boudin. A solution with bounded expansion rate to the model of viscous pressureless gases. SIAM J. Math. Anal., 32(1):172-193 (electronic), 2000.

    [8] L. Boudin and J. Mathiaud. A numerical scheme for the one-dimensional pressureless gases system. Numer. Methods Partial Differential Equations, 28(6):1729-1746, 2012.

    [9] Y. Brenier. A modified least action principle allowing mass concentrations for the early universe reconstruction problem. Confluentes Math., 3(3):361-385, 2011.

    [10] Y. Brenier and E. Grenier. Sticky particles and scalar conservation laws. SIAM J. Numer. Anal., 35(6):2317-2328 (electronic), 1998.

  • Metrics
    No metrics available
Share - Bookmark