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Volumn 24, Issue 3, 2000, Pages 275-298

Front tracking for one-dimensional quasilinear hyperbolic equations with variable coefficients

Author keywords

Error analysis; Front tracking; Numerical methods; Scalar conservation laws; Variable coefficients

Indexed keywords


EID: 23044523366     PISSN: 10171398     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (6)

References (35)
  • 1
    • 27144443898 scopus 로고
    • Swap - A computer program for shock wave analysis
    • Sandia Nat. Labs., Albuquerque, NM
    • L.M. Barker, Swap - a computer program for shock wave analysis, Technical Report No. SC4796(RR), Sandia Nat. Labs., Albuquerque, NM (1963).
    • (1963) Technical Report No. SC4796(RR)
    • Barker, L.M.1
  • 2
  • 3
    • 0006338644 scopus 로고    scopus 로고
    • Well-posedness of the Cauchy problem for n × n systems of conservation laws
    • to appear
    • A. Bressan, G. Crasta and B. Piccoli, Well-posedness of the Cauchy problem for n × n systems of conservation laws, Mem. Amer. Math. Soc., to appear.
    • Mem. Amer. Math. Soc.
    • Bressan, A.1    Crasta, G.2    Piccoli, B.3
  • 4
    • 0031295331 scopus 로고    scopus 로고
    • Uniqueness of weak solutions to systems of conservation laws
    • A. Bressan and P. LeFloch, Uniqueness of weak solutions to systems of conservation laws, Arch. Rational Mech. Anal. 140(4) (1997) 301-317.
    • (1997) Arch. Rational Mech. Anal. , vol.140 , Issue.4 , pp. 301-317
    • Bressan, A.1    Lefloch, P.2
  • 6
    • 0001690234 scopus 로고
    • Polygonal approximation of solutions of the initial value problem for a conservation law
    • C.M. Dafermos, Polygonal approximation of solutions of the initial value problem for a conservation law, J. Math. Anal. Appl. 38 (1972) 33-41.
    • (1972) J. Math. Anal. Appl. , vol.38 , pp. 33-41
    • Dafermos, C.M.1
  • 7
    • 0000469917 scopus 로고    scopus 로고
    • Front tracking and operator splitting for nonlinear degenerate convection-diffusion equations
    • eds. P. Bjørstad and M. Luskin, The IMA Volumes in Mathematics and its Applications, Springer, New York
    • S. Evje, K.H. Karlsen, K.-A. Lie and N.H. Risebro, Front tracking and operator splitting for nonlinear degenerate convection-diffusion equations, in: Parallel Solution of Partial Differential Equations, eds. P. Bjørstad and M. Luskin, The IMA Volumes in Mathematics and its Applications, Vol. 120 (Springer, New York, 2000) pp. 209-227.
    • (2000) Parallel Solution of Partial Differential Equations , vol.120 , pp. 209-227
    • Evje, S.1    Karlsen, K.H.2    Lie, K.-A.3    Risebro, N.H.4
  • 8
    • 21144479253 scopus 로고
    • Conservation laws with discontinuous flux function
    • T. Gimse, Conservation laws with discontinuous flux function, SIAM J. Math. Anal. 24(2) (1993) 279-289.
    • (1993) SIAM J. Math. Anal. , vol.24 , Issue.2 , pp. 279-289
    • Gimse, T.1
  • 10
    • 0001367271 scopus 로고
    • Solution of the Cauchy problem for a conservation law with a discontinuous flux function
    • T. Gimse and N.H. Risebro, Solution of the Cauchy problem for a conservation law with a discontinuous flux function, SIAM J. Math. Anal. 23(3) (1992) 635-648.
    • (1992) SIAM J. Math. Anal. , vol.23 , Issue.3 , pp. 635-648
    • Gimse, T.1    Risebro, N.H.2
  • 12
    • 1542783186 scopus 로고
    • Some numerical experiments with Dafermos's method for nonlinear hyperbolic equations
    • Tagung, Math. Forschungsinstitut, Oberwolfach (1971), Lecture Notes in Mathematics, Springer, Berlin
    • G.W. Hedstrom, Some numerical experiments with Dafermos's method for nonlinear hyperbolic equations, in: Numerische Lösung nichtlinearer partieller Differential- und Integrodifferentialgleichungen, Tagung, Math. Forschungsinstitut, Oberwolfach (1971), Lecture Notes in Mathematics, Vol. 267 (Springer, Berlin, 1972) pp. 117-138.
    • (1972) Numerische Lösung Nichtlinearer Partieller Differential- und Integrodifferentialgleichungen , vol.267 , pp. 117-138
    • Hedstrom, G.W.1
  • 13
    • 27144554434 scopus 로고
    • The accuracy of Dafermos' method for nonlinear hyperbolic equations
    • Brno (1972), Folia Fac. Sci. Natur. Univ. Purkynianae Brunensis, Ser. Monograph., Tomus 1, Purkyně Univ., Brno
    • G.W. Hedstrom, The accuracy of Dafermos' method for nonlinear hyperbolic equations, in: Proc. of Equadiff III, 3rd Czechoslovak Conf. on Differential Equations and their Applications, Brno (1972), Folia Fac. Sci. Natur. Univ. Purkynianae Brunensis, Ser. Monograph., Tomus 1, Purkyně Univ., Brno (1973) pp. 175-178.
    • (1973) Proc. of Equadiff III, 3rd Czechoslovak Conf. on Differential Equations and Their Applications , pp. 175-178
    • Hedstrom, G.W.1
  • 14
    • 0001911914 scopus 로고
    • On scalar conservation laws in one-dimension
    • eds. S. Albeverio, J.E. Fenstad, H. Holden and T. Lindstrøm Cambridge Univ. Press, Cambridge
    • H. Holden and L. Holden, On scalar conservation laws in one-dimension, in: Ideas and Methods in Mathematics and Physics, eds. S. Albeverio, J.E. Fenstad, H. Holden and T. Lindstrøm (Cambridge Univ. Press, Cambridge, 1988) pp. 480-509.
    • (1988) Ideas and Methods in Mathematics and Physics , pp. 480-509
    • Holden, H.1    Holden, L.2
  • 15
    • 0023859716 scopus 로고
    • A numerical method for first order nonlinear scalar conservation laws in one-dimension
    • H. Holden, L. Holden and R. Høegh-Krohn, A numerical method for first order nonlinear scalar conservation laws in one-dimension, Comput. Math. Appl. 15(6-8) (1988) 595-602.
    • (1988) Comput. Math. Appl. , vol.15 , Issue.6-8 , pp. 595-602
    • Holden, H.1    Holden, L.2    Høegh-Krohn, R.3
  • 17
    • 0031259147 scopus 로고    scopus 로고
    • The Buckley-Leverett equation with spatially stochastic flux function
    • L. Holden, The Buckley-Leverett equation with spatially stochastic flux function, SIAM J. Appl. Math. 57(5) (1997) 1443-1454.
    • (1997) SIAM J. Appl. Math. , vol.57 , Issue.5 , pp. 1443-1454
    • Holden, L.1
  • 18
    • 0033239110 scopus 로고    scopus 로고
    • An unconditionally stable splitting for a class of nonlinear parabolic equations
    • K.H. Karlsen and K.-A. Lie, An unconditionally stable splitting for a class of nonlinear parabolic equations, IMA J. Numer. Anal. 19(4) (1999) 609-635.
    • (1999) IMA J. Numer. Anal. , vol.19 , Issue.4 , pp. 609-635
    • Karlsen, K.H.1    Lie, K.-A.2
  • 19
    • 0031997184 scopus 로고    scopus 로고
    • A front-tracking approach to a two-phase fluid-flow model with capillary forces
    • K.H. Karlsen, K.-A. Lie, N.H. Risebro and J. Frøyen, A front-tracking approach to a two-phase fluid-flow model with capillary forces, In Situ 22(1) (1998) 59-89.
    • (1998) In Situ , vol.22 , Issue.1 , pp. 59-89
    • Karlsen, K.H.1    Lie, K.-A.2    Risebro, N.H.3    Frøyen, J.4
  • 20
    • 0000055941 scopus 로고
    • Convex conservation laws with discontinuous coefficients. Existence, uniqueness and asymptotic behavior
    • C. Klingenberg and N.H. Risebro, Convex conservation laws with discontinuous coefficients. Existence, uniqueness and asymptotic behavior, Comm. Partial Differential Equations 20(11/12) (1995) 1959-1990.
    • (1995) Comm. Partial Differential Equations , vol.20 , Issue.11-12 , pp. 1959-1990
    • Klingenberg, C.1    Risebro, N.H.2
  • 21
    • 84956238079 scopus 로고
    • First order quasi-linear equations in several independent variables
    • S.N. Kružkov, First order quasi-linear equations in several independent variables, Math. USSR-Sb. 10(2) (1970) 217-243.
    • (1970) Math. USSR-Sb. , vol.10 , Issue.2 , pp. 217-243
    • Kružkov, S.N.1
  • 22
    • 0001161125 scopus 로고
    • Accuracy of some approximative methods for computing the weak solutions of a first-order quasi-linear equation
    • N.N. Kuznetsov, Accuracy of some approximative methods for computing the weak solutions of a first-order quasi-linear equation, Comput. Math. Math. Phys. 16(6) (1976) 105-119.
    • (1976) Comput. Math. Math. Phys. , vol.16 , Issue.6 , pp. 105-119
    • Kuznetsov, N.N.1
  • 23
    • 0030173370 scopus 로고    scopus 로고
    • On an implementation of a front tracking method for hyperbolic conservation laws
    • J.O. Langseth, On an implementation of a front tracking method for hyperbolic conservation laws, Adv. in Engrg. Software 26(1) (1996) 45-63.
    • (1996) Adv. in Engrg. Software , vol.26 , Issue.1 , pp. 45-63
    • Langseth, J.O.1
  • 24
    • 0000814807 scopus 로고
    • Large time step shock-capturing techniques for scalar conservation laws
    • R.J. LeVeque, Large time step shock-capturing techniques for scalar conservation laws, SIAM J. Numer. Anal. 19(6) (1982) 1091-1109.
    • (1982) SIAM J. Numer. Anal. , vol.19 , Issue.6 , pp. 1091-1109
    • Leveque, R.J.1
  • 25
    • 0022388409 scopus 로고
    • A large time step generalization of Godunov's method for systems of conservation laws
    • R.J. LeVeque, A large time step generalization of Godunov's method for systems of conservation laws, SIAM J. Numer. Anal. 22(6) (1985) 1051-1073.
    • (1985) SIAM J. Numer. Anal. , vol.22 , Issue.6 , pp. 1051-1073
    • Leveque, R.J.1
  • 26
    • 0000397010 scopus 로고    scopus 로고
    • A dimensional splitting method for nonlinear equations with variable coefficients
    • K.-A. Lie, A dimensional splitting method for nonlinear equations with variable coefficients, BIT 39(4) (1999) 683-700.
    • (1999) BIT , vol.39 , Issue.4 , pp. 683-700
    • Lie, K.-A.1
  • 27
    • 0001844855 scopus 로고
    • A moving mesh numerical method for hyperbolic conservation laws
    • B.J. Lucier, A moving mesh numerical method for hyperbolic conservation laws, Math. Comp. 46(173) (1986) 59-69.
    • (1986) Math. Comp. , vol.46 , Issue.173 , pp. 59-69
    • Lucier, B.J.1
  • 28
    • 0002717472 scopus 로고
    • Discontinuous solutions of non-linear differential equations
    • O.A. Oleinik, Discontinuous solutions of non-linear differential equations, Amer. Math. Soc. Transl. Ser. 2 26 (1963) 95-172.
    • (1963) Amer. Math. Soc. Transl. Ser. 2 , vol.26 , pp. 95-172
    • Oleinik, O.A.1
  • 29
    • 0001354424 scopus 로고
    • Uniqueness and stability of the generalized solution of the Cauchy problem for a quasi-linear equation
    • O.A. Oleinik, Uniqueness and stability of the generalized solution of the Cauchy problem for a quasi-linear equation, Amen Math. Soc. Transl. Ser. 2 33 (1963) 285-290.
    • (1963) Amen Math. Soc. Transl. Ser. 2 , vol.33 , pp. 285-290
    • Oleinik, O.A.1
  • 30
    • 84966257267 scopus 로고
    • A front-tracking alternative to the random choice method
    • N.H. Risebro, A front-tracking alternative to the random choice method, Proc. Amer. Math. Soc. 117(4)(1993) 1125-1139.
    • (1993) Proc. Amer. Math. Soc. , vol.117 , Issue.4 , pp. 1125-1139
    • Risebro, N.H.1
  • 31
    • 0001502445 scopus 로고
    • Front tracking applied to a nonstrictly hyperbolic system of conservation laws
    • N.H. Risebro and A. Tveito, Front tracking applied to a nonstrictly hyperbolic system of conservation laws, SIAM J. Ser. Statist. Comput. 12(6) (1991) 1401-1419.
    • (1991) SIAM J. Ser. Statist. Comput , vol.12 , Issue.6 , pp. 1401-1419
    • Risebro, N.H.1    Tveito, A.2
  • 32
    • 0001027457 scopus 로고
    • A front tracking method for conservation laws in one dimension
    • N.H. Risebro and A. Tveito, A front tracking method for conservation laws in one dimension, J. Comput. Phys. 101(1) (1992) 130-139.
    • (1992) J. Comput. Phys. , vol.101 , Issue.1 , pp. 130-139
    • Risebro, N.H.1    Tveito, A.2
  • 33
    • 38249040792 scopus 로고
    • AZTEC: A front tracking code based on Godunov's method
    • B.K. Swartz and B. Wendroff, AZTEC: a front tracking code based on Godunov's method, Appl. Numer. Math. 2(3-5) (1986) 385-397.
    • (1986) Appl. Numer. Math. , vol.2 , Issue.3-5 , pp. 385-397
    • Swartz, B.K.1    Wendroff, B.2
  • 34
    • 0000526422 scopus 로고
    • Existence, uniqueness, and continuous dependence for a system of hyperbolic equations modeling polymer flooding
    • A. Tveito and R. Winther, Existence, uniqueness, and continuous dependence for a system of hyperbolic equations modeling polymer flooding, SIAM J. Math. Anal. 22(4) (1991) 905-933.
    • (1991) SIAM J. Math. Anal. , vol.22 , Issue.4 , pp. 905-933
    • Tveito, A.1    Winther, R.2
  • 35
    • 27144533499 scopus 로고
    • A note on Dafermos' polygonal approximation method
    • in Chinese
    • Y.S. Zheng, A note on Dafermos' polygonal approximation method, J. Math. Res. Exposition 4(1) (1984) 65-66 (in Chinese).
    • (1984) J. Math. Res. Exposition , vol.4 , Issue.1 , pp. 65-66
    • Zheng, Y.S.1


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