메뉴 건너뛰기




Volumn 68, Issue 227, 1999, Pages 1025-1055

Generalized monotone schemes, discrete paths of extrema, and discrete entropy conditions

Author keywords

Conservation law; Entropy solution; Extremum path; High order accuracy; Monotone scheme; MUSCL scheme

Indexed keywords


EID: 0041169211     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0025-5718-99-01062-5     Document Type: Article
Times cited : (22)

References (76)
  • 1
    • 0030509253 scopus 로고    scopus 로고
    • A MUSCL methods satisfying all the numerical entropy inequalities
    • F. Bouchut, C. Bourdarias, and B. Perthame, A MUSCL methods satisfying all the numerical entropy inequalities, Math. Comp. 65 (1996), 1439-1461. MR 97a:65080
    • (1996) Math. Comp. , vol.65 , pp. 1439-1461
    • Bouchut, F.1    Bourdarias, C.2    Perthame, B.3
  • 2
    • 0030509253 scopus 로고    scopus 로고
    • F. Bouchut, C. Bourdarias, and B. Perthame, A MUSCL methods satisfying all the numerical entropy inequalities, Math. Comp. 65 (1996), 1439-1461. MR 97a:65080
    • MR , vol.97 A , pp. 65080
  • 3
    • 0003094692 scopus 로고
    • The one-sided Lipschitz condition for convex scalar conservation laws
    • Y. Brenier and S. J. Osher, The one-sided Lipschitz condition for convex scalar conservation laws, SIAM J. Numer. Anal. 25 (1988), 8-23. MR 89a:65134
    • (1988) SIAM J. Numer. Anal. , vol.25 , pp. 8-23
    • Brenier, Y.1    Osher, S.J.2
  • 4
    • 0039660504 scopus 로고    scopus 로고
    • Y. Brenier and S. J. Osher, The one-sided Lipschitz condition for convex scalar conservation laws, SIAM J. Numer. Anal. 25 (1988), 8-23. MR 89a:65134
    • MR , vol.89 A , pp. 65134
  • 5
    • 0002162479 scopus 로고    scopus 로고
    • Global solutions of the Cauchy problem for quasilinear first order equations in several space variables
    • E. Conway and J.A. Smoller, Global solutions of the Cauchy problem for quasilinear first order equations in several space variables, Comm. Pure Appl. Math. 19 (1966), 95-105. MR 33:388
    • (1966) Comm. Pure Appl. Math. , vol.19 , pp. 95-105
    • Conway, E.1    Smoller, J.A.2
  • 6
    • 0002162479 scopus 로고    scopus 로고
    • E. Conway and J.A. Smoller, Global solutions of the Cauchy problem for quasilinear first order equations in several space variables, Comm. Pure Appl. Math. 19 (1966), 95-105. MR 33:388
    • MR , vol.33 , pp. 388
  • 7
    • 0030501943 scopus 로고    scopus 로고
    • An entropy satisfying MUSCL scheme for systems of conservation laws
    • F. Coquel and P.G. LeFloch, An entropy satisfying MUSCL scheme for systems of conservation laws, Numer. Math. 74 (1996), 1-33. MR 97g:65179
    • (1996) Numer. Math. , vol.74 , pp. 1-33
    • Coquel, F.1    LeFloch, P.G.2
  • 8
    • 0030501943 scopus 로고    scopus 로고
    • F. Coquel and P.G. LeFloch, An entropy satisfying MUSCL scheme for systems of conservation laws, Numer. Math. 74 (1996), 1-33. MR 97g:65179
    • MR , vol.97 G , pp. 65179
  • 9
    • 0000480805 scopus 로고
    • A direct Eulerian MUSCL scheme for gas dynamics
    • P. Colella, A direct Eulerian MUSCL scheme for gas dynamics, SIAM J. Sci. Stat. Comput. 6 (1985), 104-117. MR 86g:65156
    • (1985) SIAM J. Sci. Stat. Comput. , vol.6 , pp. 104-117
    • Colella, P.1
  • 10
    • 0039705818 scopus 로고    scopus 로고
    • P. Colella, A direct Eulerian MUSCL scheme for gas dynamics, SIAM J. Sci. Stat. Comput. 6 (1985), 104-117. MR 86g:65156
    • MR , vol.86 G , pp. 65156
  • 11
    • 84966217981 scopus 로고    scopus 로고
    • Monotone difference approximations for scalar conservation laws
    • M.G. Crandall and A. Majda, Monotone difference approximations for scalar conservation laws, Math, of Comp. 34 (1980), 1-21. MR 81b:65079
    • (1980) Math, of Comp. , vol.34 , pp. 1-21
    • Crandall, M.G.1    Majda, A.2
  • 12
    • 84966217981 scopus 로고    scopus 로고
    • M.G. Crandall and A. Majda, Monotone difference approximations for scalar conservation laws, Math, of Comp. 34 (1980), 1-21. MR 81b:65079
    • MR , vol.81 B , pp. 65079
  • 13
    • 0040564034 scopus 로고
    • Generalized characteristics in hyperbolic conservation laws: A study of the structure and the asymptotic behavior of solutions
    • ed. R.J. Knops, Res. Notes in Math., Pitman, London
    • C.M. Dafermos, Generalized characteristics in hyperbolic conservation laws: a study of the structure and the asymptotic behavior of solutions, in "Nonlinear Analysis and Mechanics: Heriot-Watt symposium", ed. R.J. Knops, Res. Notes in Math., vol. 17, Pitman, London, 1977, pp. 1-58. MR 58:1693
    • (1977) Nonlinear Analysis and Mechanics: Heriot-Watt Symposium , vol.17 , pp. 1-58
    • Dafermos, C.M.1
  • 14
    • 0040297676 scopus 로고    scopus 로고
    • C.M. Dafermos, Generalized characteristics in hyperbolic conservation laws: a study of the structure and the asymptotic behavior of solutions, in "Nonlinear Analysis and Mechanics: Heriot-Watt symposium", ed. R.J. Knops, Res. Notes in Math., vol. 17, Pitman, London, 1977, pp. 1-58. MR 58:1693
    • MR , vol.58 , pp. 1693
  • 15
    • 84966208277 scopus 로고    scopus 로고
    • One-sided difference approximations for nonlinear conservation laws
    • B. Engquist and S.J. Osher, One-sided difference approximations for nonlinear conservation laws, Math. Comp. 36 (1981), 321-351. MR 82c:65056
    • (1981) Math. Comp. , vol.36 , pp. 321-351
    • Engquist, B.1    Osher, S.J.2
  • 16
    • 84966208277 scopus 로고    scopus 로고
    • B. Engquist and S.J. Osher, One-sided difference approximations for nonlinear conservation laws, Math. Comp. 36 (1981), 321-351. MR 82c:65056
    • MR , vol.82 C , pp. 65056
  • 17
    • 0002299780 scopus 로고
    • Differential equations with discontinuous right-hand side
    • A.F. Filippov, Differential equations with discontinuous right-hand side, Mat. Sb. 51 (1960), 99-128; English transl., Amer. Math. Soc. Transl. (2) 42 (1964), 199-231. MR 22:4846
    • (1960) Mat. Sb. , vol.51 , pp. 99-128
    • Filippov, A.F.1
  • 18
    • 0002299782 scopus 로고
    • English transl.
    • A.F. Filippov, Differential equations with discontinuous right-hand side, Mat. Sb. 51 (1960), 99-128; English transl., Amer. Math. Soc. Transl. (2) 42 (1964), 199-231. MR 22:4846
    • (1964) Amer. Math. Soc. Transl. (2) , vol.42 , pp. 199-231
  • 19
    • 0040891840 scopus 로고    scopus 로고
    • A.F. Filippov, Differential equations with discontinuous right-hand side, Mat. Sb. 51 (1960), 99-128; English transl., Amer. Math. Soc. Transl. (2) 42 (1964), 199-231. MR 22:4846
    • MR , vol.22 , pp. 4846
  • 20
    • 0003325997 scopus 로고
    • Decay of solutions of nonlinear hyperbolic conservation laws
    • J. Glimm and P.D. Lax, Decay of solutions of nonlinear hyperbolic conservation laws, Mem. Amer. Math. Soc 101 (1970). MR 42:676
    • (1970) Mem. Amer. Math. Soc , vol.101
    • Glimm, J.1    Lax, P.D.2
  • 21
    • 0040891841 scopus 로고    scopus 로고
    • J. Glimm and P.D. Lax, Decay of solutions of nonlinear hyperbolic conservation laws, Mem. Amer. Math. Soc 101 (1970). MR 42:676
    • MR , vol.42 , pp. 676
  • 22
    • 0001082359 scopus 로고
    • Hyperbolic systems of conservation laws
    • Ellipses, Paris
    • E. Godlewski and P.-A. Raviart, Hyperbolic Systems of Conservation Laws, Math. & Appl., no. 3/4, Ellipses, Paris, 1991. MR 45i:65146
    • (1991) Math. & Appl. , Issue.3-4
    • Godlewski, E.1    Raviart, P.-A.2
  • 23
    • 0040297672 scopus 로고    scopus 로고
    • E. Godlewski and P.-A. Raviart, Hyperbolic Systems of Conservation Laws, Math. & Appl., no. 3/4, Ellipses, Paris, 1991. MR 45i:65146
    • MR , vol.45 I , pp. 65146
  • 24
    • 0000296272 scopus 로고
    • A geometric approach to high resolution TVD schemes
    • J. Goodman and R. LeVeque, A geometric approach to high resolution TVD schemes, SIAM J. Numer. Anal. 25 (1988), 268-284. MR 89c:65097
    • (1988) SIAM J. Numer. Anal. , vol.25 , pp. 268-284
    • Goodman, J.1    LeVeque, R.2
  • 25
    • 0039705817 scopus 로고    scopus 로고
    • J. Goodman and R. LeVeque, A geometric approach to high resolution TVD schemes, SIAM J. Numer. Anal. 25 (1988), 268-284. MR 89c:65097
    • MR , vol.89 C , pp. 65097
  • 26
    • 0021381876 scopus 로고    scopus 로고
    • On a class of high order resolution total-variation-stable finite-difference schemes
    • A. Harten, On a class of high order resolution total-variation-stable finite-difference schemes, SIAM J. Numer. Anal. 21 (1974), 1-23. MR 85f:65085
    • (1974) SIAM J. Numer. Anal. , vol.21 , pp. 1-23
    • Harten, A.1
  • 27
    • 0021381876 scopus 로고    scopus 로고
    • A. Harten, On a class of high order resolution total-variation-stable finite-difference schemes, SIAM J. Numer. Anal. 21 (1974), 1-23. MR 85f:65085
    • MR , vol.85 F , pp. 65085
  • 28
    • 40749159424 scopus 로고    scopus 로고
    • High resolution schemes for hyperbolic conservation laws
    • A. Harten, High resolution schemes for hyperbolic conservation laws, J. Comput. Phys. 49 (1983), 357-393. MR 84g:65115
    • (1983) J. Comput. Phys. , vol.49 , pp. 357-393
    • Harten, A.1
  • 29
    • 40749159424 scopus 로고    scopus 로고
    • A. Harten, High resolution schemes for hyperbolic conservation laws, J. Comput. Phys. 49 (1983), 357-393. MR 84g:65115
    • MR , vol.84 G , pp. 65115
  • 30
    • 33749725182 scopus 로고    scopus 로고
    • Uniformly high order accurate essentially non-oscillatory schemes
    • A. Harten, B. Engquist, S. Osher and S. Chakravarthy, Uniformly high order accurate essentially non-oscillatory schemes, J. Comput. Phys. 71 (1987), 231-303. MR 90a:65119
    • (1987) J. Comput. Phys. , vol.71 , pp. 231-303
    • Harten, A.1    Engquist, B.2    Osher, S.3    Chakravarthy, S.4
  • 31
    • 33749725182 scopus 로고    scopus 로고
    • A. Harten, B. Engquist, S. Osher and S. Chakravarthy, Uniformly high order accurate essentially non-oscillatory schemes, J. Comput. Phys. 71 (1987), 231-303. MR 90a:65119
    • MR , vol.90 A , pp. 65119
  • 32
    • 84980170156 scopus 로고    scopus 로고
    • On finite-difference approximations and entropy conditions for shocks
    • A. Harten, J.M. Hyman and P.D. Lax, On finite-difference approximations and entropy conditions for shocks, Comm. Pure Appl. Math. 29 (1976), 297-322. MR 54:1640
    • (1976) Comm. Pure Appl. Math. , vol.29 , pp. 297-322
    • Harten, A.1    Hyman, J.M.2    Lax, P.D.3
  • 33
    • 84980170156 scopus 로고    scopus 로고
    • A. Harten, J.M. Hyman and P.D. Lax, On finite-difference approximations and entropy conditions for shocks, Comm. Pure Appl. Math. 29 (1976), 297-322. MR 54:1640
    • MR , vol.54 , pp. 1640
  • 34
    • 84968487025 scopus 로고    scopus 로고
    • On cell entropy inequality for discontinuous Galerkin methods
    • G. Jiang and C.-W. Shu, On cell entropy inequality for discontinuous Galerkin methods, Math. Comp. 62 (1994), 531-538. MR 94h:65099
    • (1994) Math. Comp. , vol.62 , pp. 531-538
    • Jiang, G.1    Shu, C.-W.2
  • 35
    • 84968487025 scopus 로고    scopus 로고
    • G. Jiang and C.-W. Shu, On cell entropy inequality for discontinuous Galerkin methods, Math. Comp. 62 (1994), 531-538. MR 94h:65099
    • MR , vol.94 H , pp. 65099
  • 37
    • 84980136413 scopus 로고    scopus 로고
    • 1 contractive semigroup, Comm Pure Appl. Math. 24 (1971), 125-132. MR 42:6428
    • MR , vol.42 , pp. 6428
  • 38
    • 84956238079 scopus 로고    scopus 로고
    • First order quasilinear equations in several independent variables
    • S.N. Kružkov, First order quasilinear equations in several independent variables, Math. USSR Sbornik 10 (1970), 217-243. MR 42:2159
    • (1970) Math. USSR Sbornik , vol.10 , pp. 217-243
    • Kružkov, S.N.1
  • 39
    • 84956238079 scopus 로고    scopus 로고
    • S.N. Kružkov, First order quasilinear equations in several independent variables, Math. USSR Sbornik 10 (1970), 217-243. MR 42:2159
    • MR , vol.42 , pp. 2159
  • 40
    • 84980077727 scopus 로고    scopus 로고
    • Hyperbolic systems of conservation laws II
    • P.D. Lax, Hyperbolic systems of conservation laws II, Comm. Pure Appl. Math. 10 (1957), 537-566. MR 20:176
    • (1957) Comm. Pure Appl. Math. , vol.10 , pp. 537-566
    • Lax, P.D.1
  • 41
    • 84980077727 scopus 로고    scopus 로고
    • P.D. Lax, Hyperbolic systems of conservation laws II, Comm. Pure Appl. Math. 10 (1957), 537-566. MR 20:176
    • MR , vol.20 , pp. 176
  • 42
    • 0003308121 scopus 로고
    • Hyperbolic systems of conservation laws and the mathematical theory of shock waves
    • Philadelphia
    • P.D. Lax, Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves, SIAM, Philadelphia, 1973. MR 50:2709
    • (1973) SIAM
    • Lax, P.D.1
  • 43
    • 0040891837 scopus 로고    scopus 로고
    • P.D. Lax, Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves, SIAM, Philadelphia, 1973. MR 50:2709
    • MR , vol.50 , pp. 2709
  • 44
    • 84980077199 scopus 로고    scopus 로고
    • Systems of conservation laws
    • P.D. Lax and B. Wendroff, Systems of conservation laws, Comm. Pure Appl. Math. 13 (1960), 217-237. MR 22:11523
    • (1960) Comm. Pure Appl. Math. , vol.13 , pp. 217-237
    • Lax, P.D.1    Wendroff, B.2
  • 45
    • 84980077199 scopus 로고    scopus 로고
    • P.D. Lax and B. Wendroff, Systems of conservation laws, Comm. Pure Appl. Math. 13 (1960), 217-237. MR 22:11523
    • MR , vol.22 , pp. 11523
  • 46
    • 34249988639 scopus 로고
    • Towards the ultimate conservative difference scheme, II, Monotonicity and conservation combined in a second order scheme
    • B. van Leer, Towards the ultimate conservative difference scheme, II, Monotonicity and conservation combined in a second order scheme, J. Comp. Phys. 14 (1974), 361-370.
    • (1974) J. Comp. Phys. , vol.14 , pp. 361-370
    • Van Leer, B.1
  • 47
    • 2442433925 scopus 로고
    • Towards the ultimate conservative difference scheme, V, A second order sequel to Godunov's method
    • B. van Leer, Towards the ultimate conservative difference scheme, V, A second order sequel to Godunov's method, J. Comp. Phys. 32 (1979), 101-136.
    • (1979) J. Comp. Phys. , vol.32 , pp. 101-136
    • Van Leer, B.1
  • 48
    • 0040093141 scopus 로고
    • Discrete entropy and monotonicity criterion for hyperbolic conservation laws
    • P.G. LeFloch and J.G. Liu, Discrete entropy and monotonicity criterion for hyperbolic conservation laws, C.R. Acad. Sc. Paris 319 (1994), 881-886. MR 95g:65121
    • (1994) C.R. Acad. Sc. Paris , vol.319 , pp. 881-886
    • LeFloch, P.G.1    Liu, J.G.2
  • 49
    • 0039705828 scopus 로고    scopus 로고
    • P.G. LeFloch and J.G. Liu, Discrete entropy and monotonicity criterion for hyperbolic conservation laws, C.R. Acad. Sc. Paris 319 (1994), 881-886. MR 95g:65121
    • MR , vol.95 G , pp. 65121
  • 51
    • 0040686629 scopus 로고
    • Convergence of MUSCL type methods for scalar conservation laws
    • Série I
    • P.-L. Lions and P. Souganidis, Convergence of MUSCL type methods for scalar conservation laws, C.R. Acad. Sc. Paris, Série I, 311 (1990), 259-264. MR 911:65168
    • (1990) C.R. Acad. Sc. Paris , vol.311 , pp. 259-264
    • Lions, P.-L.1    Souganidis, P.2
  • 52
    • 0039705822 scopus 로고    scopus 로고
    • P.-L. Lions and P. Souganidis, Convergence of MUSCL type methods for scalar conservation laws, C.R. Acad. Sc. Paris, Série I, 311 (1990), 259-264. MR 911:65168
    • MR , vol.911 , pp. 65168
  • 53
    • 21844506272 scopus 로고    scopus 로고
    • Convergence of MUSCL and filtered schemes for scalar conservation laws and Hamilton-Jacobi equations
    • P.-L. Lions and P. Souganidis, Convergence of MUSCL and filtered schemes for scalar conservation laws and Hamilton-Jacobi equations, Numer. Math. 69 (1995), 441-470. MR 96k:65112
    • (1995) Numer. Math. , vol.69 , pp. 441-470
    • Lions, P.-L.1    Souganidis, P.2
  • 54
    • 21844506272 scopus 로고    scopus 로고
    • P.-L. Lions and P. Souganidis, Convergence of MUSCL and filtered schemes for scalar conservation laws and Hamilton-Jacobi equations, Numer. Math. 69 (1995), 441-470. MR 96k:65112
    • MR , vol.96 K , pp. 65112
  • 55
    • 0026972508 scopus 로고    scopus 로고
    • The convergence rate of approximate solutions for nonlinear scalar conservation laws
    • H. Nessyahu and E. Tadmor, The convergence rate of approximate solutions for nonlinear scalar conservation laws, SIAM J. Numer. Anal. 29 (1992), 1505-1519. MR 93j:65139
    • (1992) SIAM J. Numer. Anal. , vol.29 , pp. 1505-1519
    • Nessyahu, H.1    Tadmor, E.2
  • 56
    • 0026972508 scopus 로고    scopus 로고
    • H. Nessyahu and E. Tadmor, The convergence rate of approximate solutions for nonlinear scalar conservation laws, SIAM J. Numer. Anal. 29 (1992), 1505-1519. MR 93j:65139
    • MR , vol.93 J , pp. 65139
  • 57
    • 0028374735 scopus 로고    scopus 로고
    • The convergence rate of Godunov type schemes
    • H. Nessyahu, E. Tadmor, and T. Tamir, The convergence rate of Godunov type schemes, SIAM J. Numer. Anal. 31 (1994), 1-16. MR 94m:65140
    • (1994) SIAM J. Numer. Anal. , vol.31 , pp. 1-16
    • Nessyahu, H.1    Tadmor, E.2    Tamir, T.3
  • 58
    • 0028374735 scopus 로고    scopus 로고
    • H. Nessyahu, E. Tadmor, and T. Tamir, The convergence rate of Godunov type schemes, SIAM J. Numer. Anal. 31 (1994), 1-16. MR 94m:65140
    • MR , vol.94 M , pp. 65140
  • 59
    • 0021413939 scopus 로고    scopus 로고
    • Riemann solvers, the entropy condition and difference approximations
    • S.J. Osher, Riemann solvers, the entropy condition and difference approximations, SIAM J. Numer. Anal. 21 (1984), 217-235. MR 86d:65119
    • (1984) SIAM J. Numer. Anal. , vol.21 , pp. 217-235
    • Osher, S.J.1
  • 60
    • 0021413939 scopus 로고    scopus 로고
    • S.J. Osher, Riemann solvers, the entropy condition and difference approximations, SIAM J. Numer. Anal. 21 (1984), 217-235. MR 86d:65119
    • MR , vol.86 D , pp. 65119
  • 61
    • 0022144821 scopus 로고    scopus 로고
    • Convergence of generalized MUSCL schemes
    • S.J. Osher, Convergence of generalized MUSCL schemes, SIAM J. Numer. Anal. 22 (1985), 947-961. MR 87b:65147
    • (1985) SIAM J. Numer. Anal. , vol.22 , pp. 947-961
    • Osher, S.J.1
  • 62
    • 0022144821 scopus 로고    scopus 로고
    • S.J. Osher, Convergence of generalized MUSCL schemes, SIAM J. Numer. Anal. 22 (1985), 947-961. MR 87b:65147
    • MR , vol.87 B , pp. 65147
  • 63
    • 84966232121 scopus 로고    scopus 로고
    • On the convergence of difference approximations to scalar conservation laws
    • S.J. Osher and E. Tadmor, On the convergence of difference approximations to scalar conservation laws, Math, of Comp. 50 (1988), 19-51. MR 89m:65086
    • (1988) Math, of Comp. , vol.50 , pp. 19-51
    • Osher, S.J.1    Tadmor, E.2
  • 64
    • 84966232121 scopus 로고    scopus 로고
    • S.J. Osher and E. Tadmor, On the convergence of difference approximations to scalar conservation laws, Math, of Comp. 50 (1988), 19-51. MR 89m:65086
    • MR , vol.89 M , pp. 65086
  • 65
    • 0000564951 scopus 로고
    • Total-variation-diminishing time discretizations
    • C.W. Shu, Total-variation-diminishing time discretizations, SIAM J. Sci. Stat. Comp. 9 (1988), 1073-1084. MR 90a:65196
    • (1988) SIAM J. Sci. Stat. Comp. , vol.9 , pp. 1073-1084
    • Shu, C.W.1
  • 66
    • 0041184578 scopus 로고    scopus 로고
    • C.W. Shu, Total-variation-diminishing time discretizations, SIAM J. Sci. Stat. Comp. 9 (1988), 1073-1084. MR 90a:65196
    • MR , vol.90 A , pp. 65196
  • 67
    • 84966249400 scopus 로고    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. of Comp. 43 (1984), 369-382. MR 86g:65163
    • (1984) Math. of Comp. , vol.43 , pp. 369-382
    • Tadmor, E.1
  • 68
    • 84966249400 scopus 로고    scopus 로고
    • E. Tadmor, Numerical viscosity and the entropy condition for conservative difference schemes, Math. of Comp. 43 (1984), 369-382. MR 86g:65163
    • MR , vol.86 G , pp. 65163
  • 69
    • 0009930434 scopus 로고
    • Convenient total variation diminishing conditions for nonlinear difference schemes
    • E. Tadmor, Convenient total variation diminishing conditions for nonlinear difference schemes, SIAM J. Numer. Anal. 25 (1988), 1002-1014. MR 90b:65173
    • (1988) SIAM J. Numer. Anal. , vol.25 , pp. 1002-1014
    • Tadmor, E.1
  • 70
    • 0039705824 scopus 로고    scopus 로고
    • E. Tadmor, Convenient total variation diminishing conditions for nonlinear difference schemes, SIAM J. Numer. Anal. 25 (1988), 1002-1014. MR 90b:65173
    • MR , vol.90 B , pp. 65173
  • 71
    • 0000084910 scopus 로고
    • The space BV and quasilinear equations
    • A.I. Volpert, The space BV and quasilinear equations, Mat. Sbornik 73 (1967), 255-302; English transl., Math. USSR Sbornik 2 (1967), 225-267. MR 35:7172
    • (1967) Mat. Sbornik , vol.73 , pp. 255-302
    • Volpert, A.I.1
  • 72
    • 0001168879 scopus 로고
    • English transl.
    • A.I. Volpert, The space BV and quasilinear equations, Mat. Sbornik 73 (1967), 255-302; English transl., Math. USSR Sbornik 2 (1967), 225-267. MR 35:7172
    • (1967) Math. USSR Sbornik , vol.2 , pp. 225-267
  • 73
    • 0040252248 scopus 로고    scopus 로고
    • A.I. Volpert, The space BV and quasilinear equations, Mat. Sbornik 73 (1967), 255-302; English transl., Math. USSR Sbornik 2 (1967), 225-267. MR 35:7172
    • MR , vol.35 , pp. 7172
  • 74
    • 0030353899 scopus 로고    scopus 로고
    • On wavewise entropy inequalities for high-resolution schemes I : The semidiscrete case
    • H. Yang, On wavewise entropy inequalities for high-resolution schemes I : the semidiscrete case, Math. of Comput. 65 (1996), 45-67. MR 96d:65154
    • (1996) Math. of Comput. , vol.65 , pp. 45-67
    • Yang, H.1
  • 75
    • 0030353899 scopus 로고    scopus 로고
    • H. Yang, On wavewise entropy inequalities for high-resolution schemes I : the semidiscrete case, Math. of Comput. 65 (1996), 45-67. MR 96d:65154
    • MR , vol.96 D , pp. 65154
  • 76
    • 0043235518 scopus 로고    scopus 로고
    • On wavewise entropy inequalities for high-resolution schemes II : Fully-discrete MUSCL schemes with exact evolution in small time
    • to appear
    • H. Yang, On wavewise entropy inequalities for high-resolution schemes II : fully-discrete MUSCL schemes with exact evolution in small time, SIAM J. Numer. Anal., to appear.
    • SIAM J. Numer. Anal.
    • Yang, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.