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Convergent finite differences for 1D viscous isentropic flow in Eulerian coordinates
1. | Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, 7491, Norway |
References:
[1] |
G.-Q. Chen, D. Hoff and K. Trivisa, Global solutions of the compressible Navier-Stokes equations with large discontinuous initial data, Comm. Partial Differential Equations, 25 (2000), 2233-2257.
doi: 10.1080/03605300008821583. |
[2] |
R. Eymard, T. Gallouët, R. Herbin and J.-C. Latché, Convergence of the MAC scheme for the compressible Stokes equations, SIAM J. Numer. Anal., 48 (2010), 2218-2246.
doi: 10.1137/090779863. |
[3] |
R. Eymard, T. Gallouët, R. Herbin and J.-C. Latché, A convergent finite element-finite volume scheme for the compressible Stokes problem. Part II: The isentropic case, Math. Comp., 79 (2010), 649-675.
doi: 10.1090/S0025-5718-09-02310-2. |
[4] |
E. Feireisl., Dynamics of Viscous Compressible Fluids, Oxford Lecture Series in Mathematics and its Applications, 26, Oxford University Press, Oxford, 2004. |
[5] |
T. Gallouët, R. Herbin and J.-C. Latché, A convergent finite element-finite volume scheme for the compressible Stokes problem. Part I: The isothermal case, Math. Comp., 78 (2009), 1333-1352.
doi: 10.1090/S0025-5718-09-02216-9. |
[6] |
T. Gallouët, L. Gestaldo, R. Herbin and J.-C. Latché, An unconditionally stable pressure correction scheme for the compressible barotropic Navier-Stokes equations, M2AN Math. Model. Numer. Anal., 42 (2008), 303-331.
doi: 10.1051/m2an:2008005. |
[7] |
D. Hoff, Global existence for $1$D, compressible, isentropic Navier-Stokes equations with large initial data, Trans. Amer. Math. Soc., 303 (1987), 169-181.
doi: 10.2307/2000785. |
[8] |
H. K. Jenssen and T. K. Karper, One-dimensional compressible flow with temperature dependent transport coefficients, SIAM J. Math. Anal., 42 (2010), 904-930.
doi: 10.1137/090763135. |
[9] |
J. I. Kanel', A model system of equations for the one-dimensional motion of a gas, Differencial' nye Uravnenija., 4 (1968), 721-734. |
[10] |
K. Karlsen and T. K. Karper, A convergent nonconforming method for compressible flow, SIAM J. Numer. Anal., 48 (2010), 1847-1876.
doi: 10.1137/09076310X. |
[11] |
K. Karlsen and T. K. Karper, Convergence of a mixed method for a semi-stationary compressible Stokes system, Math. Comp., 80 (2011), 1459-1498.
doi: 10.1090/S0025-5718-2010-02446-9. |
[12] |
K. Karlsen and T. K. Karper, A convergent mixed method for the Stokes approximation of viscous compressible flow, IMA J. Numer. Anal., 32 (2011), 725-764.
doi: 10.1093/imanum/drq048. |
[13] |
T. K. Karper, A convergent FEM-DG method for the compressible Navier-Stokes equations, Numer. Math., 125 (2013), 441-510.
doi: 10.1007/s00211-013-0543-7. |
[14] |
A. V. Kazhikhov and V. V. Shelukhin, Unique global solution with respect to time of initial-boundary value problems for one-dimensional equations of a viscous gas, Prikl. Mat. Meh., 41 (1977), 282-291. |
[15] |
P.-L. Lions, Mathematical Topics in Fluid Mechanics. Vol. 2: Compressible Models, Oxford University Press, New York, 1998. |
[16] |
A. Novotný and I. Straškraba, Introduction to the Mathematical Theory of Compressible Flow, Oxford University Press, Oxford, 2004. |
[17] |
J. Serrin, Mathematical principles of classical fluid mechanics, in 1959 Handbuch der Physik (herausgegeben von S. Flügge), Bd. 8/1, Strömungsmechanik I (Mitherausgeber C. Truesdell), Springer-Verlag, Berlin-Göttingen-Heidelberg, 125-263. |
[18] |
R. Zarnowski and D. Hoff, A finite-difference scheme for the Navier-Stokes equations of one-dimensional, isentropic, compressible flow, SIAM J. Numer. Anal., 28 (1991), 78-112.
doi: 10.1137/0728004. |
[19] |
J. Zhao and D. Hoff, A convergent finite-difference scheme for the Navier-Stokes equations of one-dimensional, nonisentropic, compressible flow, SIAM J. Numer. Anal., 31 (1994), 1289-1311.
doi: 10.1137/0731067. |
[20] |
J. J. Zhao and D. Hoff, Convergence and error bound analysis of a finite-difference scheme for the one-dimensional Navier-Stokes equations, in Nonlinear Evolutionary Partial Differential Equations (Beijing, 1993), AMS/IP Stud. Adv. Math., 3, Amer. Math. Soc., Providence, RI, 1997, 625-631. |
show all references
References:
[1] |
G.-Q. Chen, D. Hoff and K. Trivisa, Global solutions of the compressible Navier-Stokes equations with large discontinuous initial data, Comm. Partial Differential Equations, 25 (2000), 2233-2257.
doi: 10.1080/03605300008821583. |
[2] |
R. Eymard, T. Gallouët, R. Herbin and J.-C. Latché, Convergence of the MAC scheme for the compressible Stokes equations, SIAM J. Numer. Anal., 48 (2010), 2218-2246.
doi: 10.1137/090779863. |
[3] |
R. Eymard, T. Gallouët, R. Herbin and J.-C. Latché, A convergent finite element-finite volume scheme for the compressible Stokes problem. Part II: The isentropic case, Math. Comp., 79 (2010), 649-675.
doi: 10.1090/S0025-5718-09-02310-2. |
[4] |
E. Feireisl., Dynamics of Viscous Compressible Fluids, Oxford Lecture Series in Mathematics and its Applications, 26, Oxford University Press, Oxford, 2004. |
[5] |
T. Gallouët, R. Herbin and J.-C. Latché, A convergent finite element-finite volume scheme for the compressible Stokes problem. Part I: The isothermal case, Math. Comp., 78 (2009), 1333-1352.
doi: 10.1090/S0025-5718-09-02216-9. |
[6] |
T. Gallouët, L. Gestaldo, R. Herbin and J.-C. Latché, An unconditionally stable pressure correction scheme for the compressible barotropic Navier-Stokes equations, M2AN Math. Model. Numer. Anal., 42 (2008), 303-331.
doi: 10.1051/m2an:2008005. |
[7] |
D. Hoff, Global existence for $1$D, compressible, isentropic Navier-Stokes equations with large initial data, Trans. Amer. Math. Soc., 303 (1987), 169-181.
doi: 10.2307/2000785. |
[8] |
H. K. Jenssen and T. K. Karper, One-dimensional compressible flow with temperature dependent transport coefficients, SIAM J. Math. Anal., 42 (2010), 904-930.
doi: 10.1137/090763135. |
[9] |
J. I. Kanel', A model system of equations for the one-dimensional motion of a gas, Differencial' nye Uravnenija., 4 (1968), 721-734. |
[10] |
K. Karlsen and T. K. Karper, A convergent nonconforming method for compressible flow, SIAM J. Numer. Anal., 48 (2010), 1847-1876.
doi: 10.1137/09076310X. |
[11] |
K. Karlsen and T. K. Karper, Convergence of a mixed method for a semi-stationary compressible Stokes system, Math. Comp., 80 (2011), 1459-1498.
doi: 10.1090/S0025-5718-2010-02446-9. |
[12] |
K. Karlsen and T. K. Karper, A convergent mixed method for the Stokes approximation of viscous compressible flow, IMA J. Numer. Anal., 32 (2011), 725-764.
doi: 10.1093/imanum/drq048. |
[13] |
T. K. Karper, A convergent FEM-DG method for the compressible Navier-Stokes equations, Numer. Math., 125 (2013), 441-510.
doi: 10.1007/s00211-013-0543-7. |
[14] |
A. V. Kazhikhov and V. V. Shelukhin, Unique global solution with respect to time of initial-boundary value problems for one-dimensional equations of a viscous gas, Prikl. Mat. Meh., 41 (1977), 282-291. |
[15] |
P.-L. Lions, Mathematical Topics in Fluid Mechanics. Vol. 2: Compressible Models, Oxford University Press, New York, 1998. |
[16] |
A. Novotný and I. Straškraba, Introduction to the Mathematical Theory of Compressible Flow, Oxford University Press, Oxford, 2004. |
[17] |
J. Serrin, Mathematical principles of classical fluid mechanics, in 1959 Handbuch der Physik (herausgegeben von S. Flügge), Bd. 8/1, Strömungsmechanik I (Mitherausgeber C. Truesdell), Springer-Verlag, Berlin-Göttingen-Heidelberg, 125-263. |
[18] |
R. Zarnowski and D. Hoff, A finite-difference scheme for the Navier-Stokes equations of one-dimensional, isentropic, compressible flow, SIAM J. Numer. Anal., 28 (1991), 78-112.
doi: 10.1137/0728004. |
[19] |
J. Zhao and D. Hoff, A convergent finite-difference scheme for the Navier-Stokes equations of one-dimensional, nonisentropic, compressible flow, SIAM J. Numer. Anal., 31 (1994), 1289-1311.
doi: 10.1137/0731067. |
[20] |
J. J. Zhao and D. Hoff, Convergence and error bound analysis of a finite-difference scheme for the one-dimensional Navier-Stokes equations, in Nonlinear Evolutionary Partial Differential Equations (Beijing, 1993), AMS/IP Stud. Adv. Math., 3, Amer. Math. Soc., Providence, RI, 1997, 625-631. |
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