메뉴 건너뛰기




Volumn 75, Issue 256, 2006, Pages 1735-1753

Order of convergence of second order schemes based on the minmod limiter

Author keywords

Conservation laws; Error estimates; Minmod limiter; Second order schemes

Indexed keywords


EID: 33750895015     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-06-01875-8     Document Type: Article
Times cited : (13)

References (18)
  • 1
    • 0003094692 scopus 로고
    • The one-sided Lipschitz condition for convex scalar conservation laws
    • MR0923922 (89a:65134)
    • Y. Brenier and S. Osher, The one-sided Lipschitz condition for convex scalar conservation laws, SIAM J. Numer. Anal., 25: 8-23, 1988. MR0923922 (89a:65134)
    • (1988) SIAM J. Numer. Anal. , vol.25 , pp. 8-23
    • Brenier, Y.1    Osher, S.2
  • 2
    • 0003273055 scopus 로고
    • Besov spaces and applications to difference methods for initial value problems
    • (A. Dold and B. Eckmann, eds.), Springer-Verlag, Berlin and New York. MR0461121 (57:1106)
    • P. Brenner, V. Thomée and L. B. Wahlbin, Besov spaces and applications to difference methods for initial value problems, (A. Dold and B. Eckmann, eds.) Lecture Notes in Math., vol. 434, Springer-Verlag, Berlin and New York, 1975. MR0461121 (57:1106)
    • (1975) Lecture Notes in Math. , vol.434
    • Brenner, P.1    Thomée, V.2    Wahlbin, L.B.3
  • 4
    • 0000296272 scopus 로고
    • A geometric approach to high resolution TVD schemes
    • MR0933724 (89c:65097)
    • J. Goodman and R. LeVeque, A geometric approach to high resolution TVD schemes, SIAM J. Numer. Anal., 25: 268-284, 1988. MR0933724 (89c:65097)
    • (1988) SIAM J. Numer. Anal. , vol.25 , pp. 268-284
    • Goodman, J.1    Leveque, R.2
  • 5
    • 0023329384 scopus 로고
    • Uniformly high order accurate non-oscillatory schemes, I
    • MR0881365 (90a:65198)
    • A. Harten and S. Osher, Uniformly high order accurate non-oscillatory schemes, I, SIAM J. Numer. Anal. 24: 279-309, 1987. MR0881365 (90a:65198)
    • (1987) SIAM J. Numer. Anal. , vol.24 , pp. 279-309
    • Harten, A.1    Osher, S.2
  • 6
    • 33749725182 scopus 로고
    • Uniformly high order accurate essentially non-oscillatory schemes, III
    • MR0897244 (90a:65199)
    • A. Harten, B. Enquist, S. Osher and S.R. Chakravarthy, Uniformly high order accurate essentially non-oscillatory schemes, III, J. Comp. Phys., 71: 231-303, 1987. MR0897244 (90a:65199)
    • (1987) J. Comp. Phys. , vol.71 , pp. 231-303
    • Harten, A.1    Enquist, B.2    Osher, S.3    Chakravarthy, S.R.4
  • 7
    • 0000238594 scopus 로고    scopus 로고
    • High-resolution non-oscillatory central schemes with nonstaggered grids for hyperbolic conservation laws
    • MR1655841 (99j:65145)
    • G.-S. Jiang, D. Levi, C.-T. Lin, S. Osher and E. Tadmor, High-resolution non-oscillatory central schemes with nonstaggered grids for hyperbolic conservation laws, SIAM J. Numer. Anal., 35: 2147-2169, 1998. MR1655841 (99j:65145)
    • (1998) SIAM J. Numer. Anal. , vol.35 , pp. 2147-2169
    • Jiang, G.-S.1    Levi, D.2    Lin, C.-T.3    Osher, S.4    Tadmor, E.5
  • 8
    • 0032206542 scopus 로고    scopus 로고
    • Nonoscillatory central schemes for hyperbolic conservation laws
    • MR1638064 (99f:65128)
    • G.-S. Jiang and E. Tadmor, Nonoscillatory central schemes for hyperbolic conservation laws, SIAM J. Sci. Comput., 19: 1892-1917, 1998. MR1638064 (99f:65128)
    • (1998) SIAM J. Sci. Comput. , vol.19 , pp. 1892-1917
    • Jiang, G.-S.1    Tadmor, E.2
  • 9
    • 33746943154 scopus 로고
    • p, 1 ≤ p ≤ ∞
    • Fasc. 3. MR1169221 (93i:41002)
    • p, 1 ≤ p ≤ ∞, Mathematica Balkanika, New series, Vol. 4, Fasc. 3: 258-270, 1990. MR1169221 (93i:41002)
    • (1990) Mathematica Balkanika, New Series , vol.4 , pp. 258-270
    • Kryakin, Yu.V.1
  • 10
    • 84980077199 scopus 로고
    • Systems of conservation laws
    • MR0120774 (22:11523)
    • P. Lax and B. Wendroff, Systems of conservation laws, Comm. Pure Appl. Math., 13: 217-237, 1960. MR0120774 (22:11523)
    • (1960) Comm. Pure Appl. Math. , vol.13 , pp. 217-237
    • Lax, P.1    Wendroff, B.2
  • 11
    • 27744577156 scopus 로고    scopus 로고
    • On convergence of minmod-type schemes
    • MR2139233 (2006b:65129)
    • S. Konyagin, B. Popov and O. Trifonov, On Convergence of Minmod-Type Schemes, SIAM J. Numer. Anal., 42: 1978-1997, 2005. MR2139233 (2006b:65129)
    • (2005) SIAM J. Numer. Anal. , vol.42 , pp. 1978-1997
    • Konyagin, S.1    Popov, B.2    Trifonov, O.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: 217-243, 1970.
    • (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
    • MR1756766 (2001d:65135)
    • A. Kurganov and E. Tadmor, New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations, J. Comp. Phys., 160: 241-282, 2000. MR1756766 (2001d:65135)
    • (2000) J. Comp. Phys. , vol.160 , pp. 241-282
    • Kurganov, A.1    Tadmor, E.2
  • 14
    • 28144455569 scopus 로고
    • Non-oscillatory central differencing for hyperbolic conservation laws
    • MR1047564 (91i:65157)
    • H. Nessyahu and E. Tadmor, Non-oscillatory central differencing for hyperbolic conservation laws, J. Comp. Phys., 87: 408-463, 1990. MR1047564 (91i:65157)
    • (1990) J. Comp. Phys. , vol.87 , pp. 408-463
    • Nessyahu, H.1    Tadmor, E.2
  • 15
    • 0000189454 scopus 로고    scopus 로고
    • The optimal convergence rate of monotone finite difference methods for hyperbolic conservation laws
    • MR1480382 (98j:65064)
    • F. Sabac, The optimal convergence rate of monotone finite difference methods for hyperbolic conservation laws, SIAM J. Numer. Anal., 34: 2306-2318, 1997. MR1480382 (98j:65064)
    • (1997) SIAM J. Numer. Anal. , vol.34 , pp. 2306-2318
    • Sabac, F.1
  • 16
    • 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. Comp. Phys., 5: 127-149, 1990.
    • (1990) J. Comp. Phys. , vol.5 , pp. 127-149
    • Shu, C.-W.1
  • 17
    • 0021513424 scopus 로고
    • High resolution schemes using flux limiters for hyperbolic conservation laws
    • MR0760628 (85m:65085)
    • P. Sweby, High resolution schemes using flux limiters for hyperbolic conservation laws, SIAM J. Numer. Anal., 21: 995-1011, 1984. MR0760628 (85m:65085)
    • (1984) SIAM J. Numer. Anal. , vol.21 , pp. 995-1011
    • Sweby, P.1
  • 18
    • 84968519569 scopus 로고
    • 1-errror estimate for monotone difference scheme
    • MR1270625 (95f:65176)
    • 1-errror estimate for monotone difference scheme, Math. Comp., 64: 581-589, 1995. MR1270625 (95f:65176)
    • (1995) Math. Comp. , vol.64 , pp. 581-589
    • Tang, T.1    Teng, Z.-H.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.