메뉴 건너뛰기




Volumn 40, Issue 5, 2002, Pages 1968-1992

Fully discrete, entropy conservative schemes of arbitrary order

Author keywords

Diffusion; Dispersion; Entropy conservative scheme; Finite difference scheme; Hyperbolic conservation law; Nonclassical shock; System of mixed type

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL METHODS; DIFFUSION; FINITE DIFFERENCE METHOD; NONLINEAR SYSTEMS; SHOCK WAVES;

EID: 0344896655     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S003614290240069X     Document Type: Article
Times cited : (195)

References (26)
  • 1
    • 0034538942 scopus 로고    scopus 로고
    • An analysis of higher order finite difference schemes for the acoustic wave equation
    • L. ANNE, P. JOLY, AND Q. H. TRAN, An analysis of higher order finite difference schemes for the acoustic wave equation, Comput. Geosci., 4 (2000), pp. 207-249.
    • (2000) Comput. Geosci. , vol.4 , pp. 207-249
    • Anne, L.1    Joly, P.2    Tran, Q.H.3
  • 2
    • 0008894832 scopus 로고
    • Kinetic relations and the propagation of phase boundaries in solids
    • A ABEYARATNE AND J.K. KNOWLES, Kinetic relations and the propagation of phase boundaries in solids, Arch. Ration. Mech. Anal., 114 (1991), pp. 119-154.
    • (1991) Arch. Ration. Mech. Anal. , vol.114 , pp. 119-154
    • Abeyaratne, A.1    Knowles, J.K.2
  • 3
    • 0026237436 scopus 로고
    • Implications of viscosity and strain-gradient effects for the kinetics of propagating phase boundaries in solids
    • R. ABEYARATNE AND J.K. KNOWLES, Implications of viscosity and strain-gradient effects for the kinetics of propagating phase boundaries in solids, SLAM J. Appl. Math., 51 (1991), pp. 1205-1221.
    • (1991) SLAM J. Appl. Math. , vol.51 , pp. 1205-1221
    • Abeyaratne, R.1    Knowles, J.K.2
  • 4
    • 0345276931 scopus 로고    scopus 로고
    • Convergence of non-linear algorithms for semi-linear hyperbolic systems
    • D. AREGBA-DRIOLLET AND J.M. MERCIER, Convergence of non-linear algorithms for semi-linear hyperbolic systems, Rend. Sera. Mat. Univ. Padova, 102 (1999), pp. 241-283.
    • (1999) Rend. Sera. Mat. Univ. Padova , vol.102 , pp. 241-283
    • Aregba-Driollet, D.1    Mercier, J.M.2
  • 5
    • 0040433291 scopus 로고    scopus 로고
    • A fully discrete scheme for diffusive-dispersive conservation laws
    • C. CHALONS AND P.G. LEFLOCH, A fully discrete scheme for diffusive-dispersive conservation laws, Numer. Math., 89 (2001), pp. 493-509.
    • (2001) Numer. Math. , vol.89 , pp. 493-509
    • Chalons, C.1    Lefloch, P.G.2
  • 6
    • 0002031820 scopus 로고    scopus 로고
    • High-order entropy conservative schemes and kinetic relations for van der Waals fluids
    • C. CHALONS AND P.G. LEFLOCH, High-order entropy conservative schemes and kinetic relations for van der Waals fluids, J. Comput. Phys., 167 (2001), pp. 1-23.
    • (2001) J. Comput. Phys. , vol.167 , pp. 1-23
    • Chalons, C.1    Lefloch, P.G.2
  • 7
    • 0001380483 scopus 로고
    • Systems of conservation laws with a convex extension
    • K.O. FRIEDRICH AND P.D. LAX, Systems of conservation laws with a convex extension, Proc. Nat. Acad. Sci. U.S.A., 68 (1971), pp. 1686-1688.
    • (1971) Proc. Nat. Acad. Sci. U.S.A. , vol.68 , pp. 1686-1688
    • Friedrich, K.O.1    Lax, P.D.2
  • 8
    • 0031508127 scopus 로고    scopus 로고
    • Nonclassical shocks and kinetic relations: Scalar conservation laws
    • B.T. HAYES AND P.G. LEFLOCH, Nonclassical shocks and kinetic relations: Scalar conservation laws, Arch. Ration. Mech. Anal., 139 (1997), pp. 1-56.
    • (1997) Arch. Ration. Mech. Anal. , vol.139 , pp. 1-56
    • Hayes, B.T.1    Lefloch, P.G.2
  • 9
    • 0001203812 scopus 로고    scopus 로고
    • Nonclassical shocks and kinetic relations: Finite difference schemes
    • B.T. HAYES AND P.G. LEFLOCH, Nonclassical shocks and kinetic relations: Finite difference schemes, SIAM J. Numer. Anal., 35 (1998), pp. 2169-2194.
    • (1998) SIAM J. Numer. Anal. , vol.35 , pp. 2169-2194
    • Hayes, B.T.1    Lefloch, P.G.2
  • 10
    • 0034345304 scopus 로고    scopus 로고
    • Nonclassical shock and kinetic relations: Strictly hyperbolic schemes
    • B.T. HAYES AND P.G. LEFLOCH, Nonclassical shock and kinetic relations: Strictly hyperbolic schemes, SIAM J. Math. Anal., 31 (2000), pp. 941-991.
    • (2000) SIAM J. Math. Anal. , vol.31 , pp. 941-991
    • Hayes, B.T.1    Lefloch, P.G.2
  • 11
    • 0000261039 scopus 로고
    • Traveling wave solutions of the modified Korteweg-de Vries Burgers equation
    • D. JACOBS, W.R. McKINNEY, AND M. SHEARER, Traveling wave solutions of the modified Korteweg-de Vries Burgers equation, 3. Differential Equations, 116 (1995), pp. 448-467.
    • (1995) J. Differential Equations , vol.116 , pp. 448-467
    • Jacobs, D.1    McKinney, W.R.2    Shearer, M.3
  • 12
  • 13
    • 21144471185 scopus 로고
    • Propagating phase boundaries: Formulation of the problem and existence via the Glimm scheme
    • P.G. LEFLOCH, Propagating phase boundaries: Formulation of the problem and existence via the Glimm scheme, Arch. Ration. Mech. Anal., 123 (1993), pp. 153-197.
    • (1993) Arch. Ration. Mech. Anal. , vol.123 , pp. 153-197
    • Lefloch, P.G.1
  • 14
    • 0344845552 scopus 로고    scopus 로고
    • Hyperbolic Systems of Conservation Laws: The Theory of Classical and Non-classical Shock Waves
    • Birkhäuser Verlag, Basel
    • P.G. LEFLOCH, Hyperbolic Systems of Conservation Laws: The Theory of Classical and Non-classical Shock Waves, Lectures in Mathematics ETH Zürich, Birkhäuser Verlag, Basel, 2002.
    • (2002) Lectures in Mathematics ETH Zürich
    • Lefloch, P.G.1
  • 15
    • 0001819709 scopus 로고    scopus 로고
    • An introduction to nonclassical shocks of systems of conservation laws
    • Proceedings of the International School on Hyperbolic Problems, Freiburg, Germany, Oct. 97, D. Kröner, M. Ohlberger, and C. Rohde, eds., Springer-Verlag, Berlin
    • P.G. LEFLOCH, An introduction to nonclassical shocks of systems of conservation laws, Proceedings of the International School on Hyperbolic Problems, Freiburg, Germany, Oct. 97, D. Kröner, M. Ohlberger, and C. Rohde, eds., Lect. Notes Comput. Sci. Engrg. 5, Springer-Verlag, Berlin, 1998, pp. 28-72.
    • (1998) Lect. Notes Comput. Sci. Engrg. , vol.5 , pp. 28-72
    • Lefloch, P.G.1
  • 16
    • 0000339031 scopus 로고    scopus 로고
    • High-order schemes, entropy inequalities and nonclassical shocks
    • P.G. LEFLOCH AND C. ROHDE, High-order schemes, entropy inequalities and nonclassical shocks, SIAM J. Numer. Anal., 37 (2000), pp. 2023-2060.
    • (2000) SIAM J. Numer. Anal. , vol.37 , pp. 2023-2060
    • Lefloch, P.G.1    Rohde, C.2
  • 17
    • 0036990230 scopus 로고    scopus 로고
    • Non-classical Riemann solvers and kinetic relations. II. An hyperbolic-elliptic model of phase transitions
    • P.G. LEFLOCH AND M.D. THANH, Non-classical Riemann solvers and kinetic relations. II. An hyperbolic-elliptic model of phase transitions, Proc. Roy. Soc. Edinburgh Sect. A, 132 (2001), pp. 181-219.
    • (2001) Proc. Roy. Soc. Edinburgh Sect. A , vol.132 , pp. 181-219
    • Lefloch, P.G.1    Thanh, M.D.2
  • 18
    • 0010791101 scopus 로고    scopus 로고
    • Global continuous Riemann solver for nonlinear elasticity
    • J.M. MERCIER AND B. PICCOLI, Global continuous Riemann solver for nonlinear elasticity, Arch. Ration. Mech. Anal., 156 (2001), pp. 89-119.
    • (2001) Arch. Ration. Mech. Anal. , vol.156 , pp. 89-119
    • Mercier, J.M.1    Piccoli, B.2
  • 19
    • 0001486653 scopus 로고
    • The Riemann problem for a class of conservation laws of mixed type
    • M. SHEARER, The Riemann problem for a class of conservation laws of mixed type, J. Differential Equations, 46 (1982), pp. 426-443.
    • (1982) J. Differential Equations , vol.46 , pp. 426-443
    • Shearer, M.1
  • 20
    • 0001648070 scopus 로고
    • Convergence of solutions to nonlinear dispersive equations
    • M.E. SCHONBEK, Convergence of solutions to nonlinear dispersive equations, Comm. Partial Differential Equations, 7 (1982), pp. 959-1000.
    • (1982) Comm. Partial Differential Equations , vol.7 , pp. 959-1000
    • Schonbek, M.E.1
  • 21
    • 0000799725 scopus 로고
    • Entropy production in second-order three-point schemes
    • T. SONAH, Entropy production in second-order three-point schemes, Numer. Math., 62 (1992), pp. 371-390.
    • (1992) Numer. Math. , vol.62 , pp. 371-390
    • Sonah, T.1
  • 22
    • 0000765110 scopus 로고
    • Numerical solution of a Klein Gordon equation
    • W. STRAUSS AND L. VASQUEZ, Numerical solution of a Klein Gordon equation, 3. Comput. Phys., 28 (1978), pp. 271-278.
    • (1978) J. Comput. Phys. , vol.28 , pp. 271-278
    • Strauss, W.1    Vasquez, L.2
  • 23
    • 84966249400 scopus 로고
    • Numerical viscosity and the entropy condition for conservative difference schemes
    • E. TADMOR, Numerical viscosity and the entropy condition for conservative difference schemes, Math. Comput., 43 (1984), pp. 369-381.
    • (1984) Math. Comput. , vol.43 , pp. 369-381
    • Tadmor, E.1
  • 24
    • 0022890030 scopus 로고
    • Entropy conservative finite element schemes
    • Numerical Methods for Compressible Flows - Finite Difference, Element and Volume Techniques, T.E. Tezduyar and T.J.R. Hughes, eds., ASME, New York
    • E. TADMOR, Entropy conservative finite element schemes, in Numerical Methods for Compressible Flows - Finite Difference, Element and Volume Techniques, Proceedings of the Winter Annual Meeting, AMD 78, T.E. Tezduyar and T.J.R. Hughes, eds., ASME, New York, 1986, pp. 149-158.
    • (1986) Proceedings of the Winter Annual Meeting , vol.AMD 78 , pp. 149-158
    • Tadmor, E.1
  • 25
    • 0000546289 scopus 로고
    • The numerical viscosity of entropy stable schemes for systems of conservation laws
    • E. TADMOR, The numerical viscosity of entropy stable schemes for systems of conservation laws, Math. Comput., 49 (1987), pp. 91-103.
    • (1987) Math. Comput. , vol.49 , pp. 91-103
    • Tadmor, E.1
  • 26
    • 2442677705 scopus 로고
    • Dynamics of non-equilibrium phase boundaries in a heat conducting non-linear elastic medium
    • L. TRUSKINOVSKY, Dynamics of non-equilibrium phase boundaries in a heat conducting non-linear elastic medium, 3. Appl. Math. Mech., 51 (1987), pp. 777-784.
    • (1987) J. Appl. Math. Mech. , vol.51 , pp. 777-784
    • Truskinovsky, L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.