메뉴 건너뛰기




Volumn 66, Issue 219, 1997, Pages 1027-1053

Convergence of difference schemes with high resolution for conservation laws

Author keywords

Conservation laws; Convergence; Entropy solution; Lax Wendroff scheme

Indexed keywords


EID: 0031490953     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0025-5718-97-00859-4     Document Type: Article
Times cited : (8)

References (32)
  • 1
    • 33749583060 scopus 로고
    • Flux corrected transport. I. SHASTA, a fluid transport algorithm that works
    • J.P. Boris and D.L. Book, Flux corrected transport. I. SHASTA, a fluid transport algorithm that works, J. Comp. Phys. 11 (1973), 38-69.
    • (1973) J. Comp. Phys. , vol.11 , pp. 38-69
    • Boris, J.P.1    Book, D.L.2
  • 3
    • 0024481658 scopus 로고
    • A study on application approaches of the theory of compensated compactness
    • MR 90h:35024
    • G.-Q. Chen and Y.-G. Lu, A study on application approaches of the theory of compensated compactness, Chinese Science Bulletin 34 (1989), 15-19. MR 90h:35024
    • (1989) Chinese Science Bulletin , vol.34 , pp. 15-19
    • Chen, G.-Q.1    Lu, Y.-G.2
  • 4
    • 84966234654 scopus 로고
    • Convergence of finite difference schemes for conservation laws in several space variables: The corrected antidiffusive flux approach
    • MR 91m:65229
    • F. Coquel and P. Le Floch, Convergence of finite difference schemes for conservation laws in several space variables: the corrected antidiffusive flux approach, Math. Comp. 57 (1991), 169-210. MR 91m:65229
    • (1991) Math. Comp. , vol.57 , pp. 169-210
    • Coquel, F.1    Le Floch, P.2
  • 5
    • 0020499710 scopus 로고
    • Convergence of approximate solutions to conservation laws
    • MR 84k:35091
    • R. DiPerna, Convergence of approximate solutions to conservation laws, Arch. Rat. Mech. Anal. 82 (1983), 27-70. MR 84k:35091
    • (1983) Arch. Rat. Mech. Anal. , vol.82 , pp. 27-70
    • DiPerna, R.1
  • 6
    • 33749725182 scopus 로고
    • Uniformly high order accurate non-oscillatory schemes, III
    • MR 90a:65199
    • A. Harten, B. Engquist, S. Osher, and S. Chakravarthy, Uniformly high order accurate non-oscillatory schemes, III, J. Comp. Phys. 71 (1987), 231-303. MR 90a:65199
    • (1987) J. Comp. Phys. , vol.71 , pp. 231-303
    • Harten, A.1    Engquist, B.2    Osher, S.3    Chakravarthy, S.4
  • 7
    • 84980170156 scopus 로고
    • On finite-difference approximations and entropy conditions for shocks
    • MR 54:1640
    • 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
  • 8
    • 0000876320 scopus 로고
    • On upstream differencing and Godunov-type schemes for hyperbolic conservation laws
    • MR 85h:65188
    • A. Harten, P. D. Lax, and B. van Leer, On upstream differencing and Godunov-type schemes for hyperbolic conservation laws, SIAM Review 25 (1983), 35. MR 85h:65188
    • (1983) SIAM Review , vol.25 , pp. 35
    • Harten, A.1    Lax, P.D.2    Van Leer, B.3
  • 10
    • 0012009827 scopus 로고
    • The generation and propagation of oscillations in dispersive IVPs and their limiting behavior
    • T. Fokas and V.E. Zakharov eds, Springer-Verlag, Berlin, MR 95c:35245
    • P.D. Lax and C.D. Levermore and S. Venakides, The generation and propagation of oscillations in dispersive IVPs and their limiting behavior. Important developments in soliton theory 1980-1990, T. Fokas and V.E. Zakharov eds, Springer-Verlag, Berlin, 1992. MR 95c:35245
    • (1992) Important Developments in Soliton Theory 1980-1990
    • Lax, P.D.1    Levermore, C.D.2    Venakides, S.3
  • 11
    • 84980077199 scopus 로고
    • Systems of conservation laws
    • MR 22:11523
    • 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
  • 12
    • 0040686629 scopus 로고
    • Convergence of MUSCL type methods for scalar conservation laws
    • MR 911:65168
    • P.L. Lions and P. Souganidis, Convergence of MUSCL type methods for scalar conservation laws, C. R. Acad. Sci. Paris, Série I 311 (1990), 259-264. MR 911:65168
    • (1990) C. R. Acad. Sci. Paris, Série I , vol.311 , pp. 259-264
    • Lions, P.L.1    Souganidis, P.2
  • 13
    • 0000334985 scopus 로고
    • The effect of viscosity in hyperbolicity impact cratering
    • R.W. MacCormack, The effect of viscosity in hyperbolicity impact cratering, AIAA Paper (1969), 69 354.
    • (1969) AIAA Paper , pp. 69-354
    • MacCormack, R.W.1
  • 14
    • 0012323913 scopus 로고
    • A systematic approach for correcting nonlinear instability: The Lax-Wendroff scheme for scalar conservation laws
    • MR 80g:65101
    • A. Majda and S. Osher, A systematic approach for correcting nonlinear instability: the Lax-Wendroff scheme for scalar conservation laws, Num. Math. 30 (1978), 429-452. MR 80g:65101
    • (1978) Num. Math. , vol.30 , pp. 429-452
    • Majda, A.1    Osher, S.2
  • 15
    • 84980186730 scopus 로고
    • Numerical viscosity and the entropy condition
    • MR 80j:65031
    • A. Majda and S. Osher, Numerical viscosity and the entropy condition, Comm. Pure Appl. Math. 32 (1979), 797-838. MR 80j:65031
    • (1979) Comm. Pure Appl. Math. , vol.32 , pp. 797-838
    • Majda, A.1    Osher, S.2
  • 16
    • 84990602715 scopus 로고
    • An alternative proof of DiPerna's theorem
    • MR 92m:35165
    • C.S. Morawetz, An alternative proof of DiPerna's theorem, Comm. Pure Appl. Math. 44 (1991), 1081-1090. MR 92m:35165
    • (1991) Comm. Pure Appl. Math. , vol.44 , pp. 1081-1090
    • Morawetz, C.S.1
  • 17
    • 0001764754 scopus 로고
    • -1.q est compacte pour tout q < 2
    • MR 83b:46045
    • -1.q est compacte pour tout q < 2, J. Math. Pures Appl. 60 (1981), 309-322. MR 83b:46045
    • (1981) J. Math. Pures Appl. , vol.60 , pp. 309-322
    • Murat, F.1
  • 18
    • 28144455569 scopus 로고
    • Non-oscillatory central differencing for hyperbolic conservation laws
    • MR 911:65157
    • H. Nessyahu and E. Tadmor, Non-oscillatory central differencing for hyperbolic conservation laws, J. Comp. Phys. 87 (1990), 408-463. MR 911:65157
    • (1990) J. Comp. Phys. , vol.87 , pp. 408-463
    • Nessyahu, H.1    Tadmor, E.2
  • 19
    • 0022144821 scopus 로고
    • On convergence of generalized MUSCL schemes
    • MR 87b:65147
    • S. Osher, On 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.1
  • 20
    • 84966232121 scopus 로고
    • On the convergence of difference, approximations to scalar conservation laws
    • MR 89m:65086
    • S. Osher and E. Tadmor, On the convergence of difference, approximations to scalar conservation laws, Math. Comp. 50 (1988), 19-51. MR 89m:65086
    • (1988) Math. Comp. , vol.50 , pp. 19-51
    • Osher, S.1    Tadmor, E.2
  • 21
    • 0026818681 scopus 로고
    • Second-order Boltzmann schemes for compressible Euler equations in one and two space, dimensions
    • MR 92m:76111
    • B. Perthame, Second-order Boltzmann schemes for compressible Euler equations in one and two space, dimensions, SIAM J. Numer. Anal. 29 (1992), 1-19. MR 92m:76111
    • (1992) SIAM J. Numer. Anal. , vol.29 , pp. 1-19
    • Perthame, B.1
  • 23
    • 0000535649 scopus 로고
    • La compacité par compensation pour les systèmes hyperboliques non linéaires de deux équations à une dimension d'espace
    • MR 88d:35123
    • D. Serre, La compacité par compensation pour les systèmes hyperboliques non linéaires de deux équations à une dimension d'espace, J. Math. Pures App . 65 (1986), 423-468. MR 88d:35123
    • (1986) J. Math. Pures App. , vol.65 , pp. 423-468
    • Serre, D.1
  • 24
    • 0001568854 scopus 로고
    • Efficient implementation of essentially non-oscillatory shock capturing schemes
    • MR 90i:65167
    • C.-W. Shu and S. Osher, Efficient implementation of essentially non-oscillatory shock capturing schemes, J. Comp. Phys. 83 (1989), 32-51 MR 90i:65167
    • (1989) J. Comp. Phys. , vol.83 , pp. 32-51
    • Shu, C.-W.1    Osher, S.2
  • 25
    • 84990556349 scopus 로고
    • Existence and stability of stationary profiles of the LW scheme
    • MR 91d:65143
    • Y.S. Smyrlis, Existence and stability of stationary profiles of the LW scheme, Comm. Pure Appl. Math. 43 (1990), 509-545. MR 91d:65143
    • (1990) Comm. Pure Appl. Math. , vol.43 , pp. 509-545
    • Smyrlis, Y.S.1
  • 26
    • 0021513424 scopus 로고
    • High resolution schemes using flux limiters for hyperbolic conservation laws
    • MR. 85m:65085
    • P.R. Sweby, High resolution schemes using flux limiters for hyperbolic conservation laws, SIAM J Num. Anal. 21 (1984), 995-1011. MR. 85m:65085
    • (1984) SIAM J Num. Anal. , vol.21 , pp. 995-1011
    • Sweby, P.R.1
  • 27
    • 0040124185 scopus 로고
    • On three-point second-order accurate conservative, dijference schemes
    • MR 89g:65115
    • T. Tang, On three-point second-order accurate conservative, dijference schemes, J. Comp. Math. 5 (1987), 105-118. MR 89g:65115
    • (1987) J. Comp. Math. , vol.5 , pp. 105-118
    • Tang, T.1
  • 28
    • 0000440966 scopus 로고
    • Compensated compactness and applications to partia differential equations
    • ed. R.J. Knops, Pitman Press, New York, MR 81m:35014
    • L. Tartar, Compensated compactness and applications to partia differential equations, Research Notes in Mathematics, Nonlinear Analysis and Mechanics, ed. R.J. Knops, vol. 4. Pitman Press, New York, 1979. MR 81m:35014
    • (1979) Research Notes in Mathematics, Nonlinear Analysis and Mechanics , vol.4
    • Tartar, L.1
  • 29
    • 0038908819 scopus 로고
    • Towards the ultimate conservative, difference schemes, V, A second order sequel to Godunov's method
    • B. van Leer, Towards the ultimate conservative, difference schemes, V, A second order sequel to Godunov's method, J. Comp. Phys. 43 (1981), 357-372.
    • (1981) J. Comp. Phys. , vol.43 , pp. 357-372
    • Van Leer, B.1
  • 30
    • 48749139407 scopus 로고
    • The numerical simulation of two dimensional fluid flow with strong shock
    • MR 85e:76004
    • P. Woodward and P. Colella, The numerical simulation of two dimensional fluid flow with strong shock, J. Comp. Phys. 54 (1984), 115-173. MR 85e:76004
    • (1984) J. Comp. Phys. , vol.54 , pp. 115-173
    • Woodward, P.1    Colella, P.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.