메뉴 건너뛰기




Volumn 42, Issue 5, 2005, Pages 1978-1997

On convergence of minmod-type schemes

Author keywords

Conservation laws; Convergence; Minmod type schemes

Indexed keywords

CONSERVATION LAWS; MINMOD-TYPE SCHEMES;

EID: 27744577156     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142903423861     Document Type: Article
Times cited : (5)

References (20)
  • 1
    • 0030509253 scopus 로고    scopus 로고
    • A MUSCL method satisfying all entropy inequalities
    • F. BOUCHUT, CH. BOURDARIAS, AND B. PERTHAME, A MUSCL method satisfying all entropy inequalities, Math. Comp., 65 (1996), pp. 1439-1461.
    • (1996) Math. Comp. , vol.65 , pp. 1439-1461
    • Bouchut, F.1    Bourdarias, Ch.2    Perthame, B.3
  • 2
    • 22044436683 scopus 로고    scopus 로고
    • Kružkov's estimates for scalar conservation laws revisited
    • F. BOUCHUT AND B. PERTHAME, Kružkov's estimates for scalar conservation laws revisited, Trans. Amer. Math. Soc., 350 (1998), pp. 2847-2870.
    • (1998) Trans. Amer. Math. Soc. , vol.350 , pp. 2847-2870
    • Bouchut, F.1    Perthame, B.2
  • 3
    • 0003094692 scopus 로고
    • The discrete one-sided Lipschitz condition for convex scalar conservation laws
    • Y. BRENIER AND S. OSHER, The discrete one-sided Lipschitz condition for convex scalar conservation laws, SIAM J. Numer. Anal., 25 (1988), pp. 8-23.
    • (1988) SIAM J. Numer. Anal. , vol.25 , pp. 8-23
    • Brenier, Y.1    Osher, S.2
  • 4
    • 0003273055 scopus 로고
    • Besov spaces and applications to difference methods for initial value problems
    • A. Dold and B. Eckmann, eds., Springer-Verlag, Berlin, New York
    • P. BRENNER, V. THOMÉE, AND L. B. WAHLBIN, Besov Spaces and Applications to Difference Methods for Initial Value Problems, Lecture Notes in Math. 434, A. Dold and B. Eckmann, eds., Springer-Verlag, Berlin, New York, 1975.
    • (1975) Lecture Notes in Math. , vol.434
    • Brenner, P.1    Thomée, V.2    Wahlbin, L.B.3
  • 6
    • 0000357991 scopus 로고
    • Uniformly high order accurate non-oscillatory schemes, i
    • A. HARTEN AND S. OSHER, Uniformly high order accurate non-oscillatory schemes, I, J. Appl. Numer. Math., 71 (1987), pp. 279-309.
    • (1987) J. Appl. Numer. Math. , vol.71 , pp. 279-309
    • Harten, A.1    Osher, S.2
  • 7
    • 33749725182 scopus 로고
    • Uniformly high order accurate essentially non-oscillatory schemes, III
    • A. HARTEN, B. ENQUIST, S. OSHER, AND S. R. CHAKRAVARTHY, Uniformly high order accurate essentially non-oscillatory schemes, III, J. Comput. Phys., 71 (1987), pp. 231-303.
    • (1987) J. Comput. Phys. , vol.71 , pp. 231-303
    • Harten, A.1    Enquist, B.2    Osher, S.3    Chakravarthy, S.R.4
  • 8
    • 0000238594 scopus 로고    scopus 로고
    • High-resolution nonoscillatory central schemes with nonstaggered grids for hyperbolic conservation laws
    • G.-S. JIANG, D. LEVY, C.-T. LIN, S. OSHER, AND E. TADMOR, High-resolution nonoscillatory central schemes with nonstaggered grids for hyperbolic conservation laws, SIAM J. Numer. Anal., 35 (1998), pp. 2147-2168.
    • (1998) SIAM J. Numer. Anal. , vol.35 , pp. 2147-2168
    • Jiang, G.-S.1    Levy, D.2    Lin, C.-T.3    Osher, S.4    Tadmor, E.5
  • 9
    • 0032206542 scopus 로고    scopus 로고
    • Nonoscillatory central schemes for multidimensional hyperbolic conservation laws
    • G.-S. JIANG AND E. TADMOR, Nonoscillatory central schemes for multidimensional hyperbolic conservation laws, SIAM J. Sci. Comput., 19 (1998), pp. 1892-1917.
    • (1998) SIAM J. Sci. Comput. , vol.19 , pp. 1892-1917
    • Jiang, G.-S.1    Tadmor, E.2
  • 10
    • 84980077199 scopus 로고
    • Systems of conservation laws
    • P. LAX AND B. WENDROFF, Systems of conservation laws, Comm. Pure Appl. Math., 13 (1960), pp. 217-237.
    • (1960) Comm. Pure Appl. Math. , vol.13 , pp. 217-237
    • Lax, P.1    Wendroff, B.2
  • 11
    • 0141976338 scopus 로고    scopus 로고
    • Weakly non-oscillatory schemes for scalar conservation laws
    • K. KOPOTUN, M. NEAMTU, AND B. POPOV, Weakly non-oscillatory schemes for scalar conservation laws, Math. Comp., 72 (2003), pp. 1747-1767.
    • (2003) Math. Comp. , vol.72 , pp. 1747-1767
    • Kopotun, K.1    Neamtu, M.2    Popov, B.3
  • 12
    • 84956238079 scopus 로고
    • First order quasi-linear equations in several independent variables
    • S. N. KRUZHKOV, First order quasi-linear equations in several independent variables, Math. USSR Sbornik, 10 (1970), pp. 217-243.
    • (1970) Math. USSR Sbornik , vol.10 , pp. 217-243
    • Kruzhkov, S.N.1
  • 13
    • 0347987814 scopus 로고    scopus 로고
    • New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations
    • A. KURGANOV AND E. TADMOR, New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations, J. Comput. Phys., 160 (2000), pp. 241-282.
    • (2000) J. Comput. Phys. , vol.160 , pp. 241-282
    • Kurganov, A.1    Tadmor, E.2
  • 14
    • 0001161125 scopus 로고
    • Accuracy of some approximate methods for computing the weak solutions of a first order quasi-linear equation
    • N. N. KUZNETSOV, Accuracy of some approximate methods for computing the weak solutions of a first order quasi-linear equation, USSR Comput. Math. Math. Phys., 16 (1976), pp. 105-119.
    • (1976) USSR Comput. Math. Math. Phys. , vol.16 , pp. 105-119
    • Kuznetsov, N.N.1
  • 15
    • 28144455569 scopus 로고
    • Non-oscillatory central differencing for hyperbolic conservation laws
    • H. NESSYAHU AND E. TADMOR, Non-oscillatory central differencing for hyperbolic conservation laws, J. Comput. Phys., 87 (1990), pp. 408-463.
    • (1990) J. Comput. Phys. , vol.87 , pp. 408-463
    • Nessyahu, H.1    Tadmor, E.2
  • 16
    • 0026972508 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), pp. 1505-1519.
    • (1992) SIAM J. Numer. Anal. , vol.29 , pp. 1505-1519
    • Nessyahu, H.1    Tadmor, E.2
  • 17
    • 0000189454 scopus 로고    scopus 로고
    • The optimal convergence rate of monotone finite difference methods for hyperbolic conservation laws
    • F. ŞABAC, The optimal convergence rate of monotone finite difference methods for hyperbolic conservation laws, SIAM J. Numer. Anal., 34 (1997), pp. 2306-2318.
    • (1997) SIAM J. Numer. Anal. , vol.34 , pp. 2306-2318
    • Şabac, F.1
  • 18
    • 0025436444 scopus 로고
    • Numerical experiments on the accuracy of ENO and modified ENO schemes
    • C.-W. SHU, Numerical experiments on the accuracy of ENO and modified ENO schemes, J. Comput. Phys., 5 (1990), pp. 127-149.
    • (1990) J. Comput. Phys. , vol.5 , pp. 127-149
    • Shu, C.-W.1
  • 19
    • 0026203648 scopus 로고
    • Local error estimates for discontinuous solutions of nonlinear hyperbolic equations
    • E. TADMOR, Local error estimates for discontinuous solutions of nonlinear hyperbolic equations, SIAM J. Numer. Anal., 28 (1991), pp. 891-906.
    • (1991) SIAM J. Numer. Anal. , vol.28 , pp. 891-906
    • Tadmor, E.1
  • 20
    • 84968519569 scopus 로고
    • 1 -error estimate for monotone difference scheme
    • 1 -error estimate for monotone difference scheme, Math. Comp., 64 (1995), pp. 581-589.
    • (1995) Math. Comp. , vol.64 , pp. 581-589
    • Tang, T.1    Teng, Z.-H.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.