메뉴 건너뛰기




Volumn 87, Issue 4, 2001, Pages 701-735

L1-stability and error estimates for approximate Hamilton-Jacobi solutions

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0035580662     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00005430     Document Type: Article
Times cited : (56)

References (38)
  • 2
    • 0003094692 scopus 로고
    • The discrete one-side Lipschitz condition for convex scalar conservation laws
    • Y. Brenier and S. Osher. The discrete one-side Lipschitz condition for convex scalar conservation laws. SIAM J. Numer. Anal. 25, 8-23 (1988)
    • (1988) SIAM J. Numer. Anal. , vol.25 , pp. 8-23
    • Brenier, Y.1    Osher, S.2
  • 4
    • 84968507121 scopus 로고
    • Some properties of viscosity solutions of Hamilton-Jacobi equations
    • M.G. Crandall, L. C. Evans, and P. L. Lions. Some properties of viscosity solutions of Hamilton-Jacobi equations. Trans. AMS 282, 487-502 (1984)
    • (1984) Trans. AMS , vol.282 , pp. 487-502
    • Crandall, M.G.1    Evans, L.C.2    Lions, P.L.3
  • 5
    • 84967708673 scopus 로고
    • User's guide to viscosity solutions of second order partial differential equations
    • M.G. Crandall, H. Ishii, and P.-L. Lions. User's guide to viscosity solutions of second order partial differential equations. Bull. AMS 27, 1-67 (1992)
    • (1992) Bull. AMS , vol.27 , pp. 1-67
    • Crandall, M.G.1    Ishii, H.2    Lions, P.-L.3
  • 6
    • 84967758647 scopus 로고
    • Viscosity solutions of Hamilton-Jacobi equations
    • M.G. Crandall and P. L. Lions. Viscosity solutions of Hamilton-Jacobi equations. Trans. AMS 277, 1-42 (1983)
    • (1983) Trans. AMS , vol.277 , pp. 1-42
    • Crandall, M.G.1    Lions, P.L.2
  • 7
    • 84966245867 scopus 로고
    • Two approximations of solutions of Hamilton-Jacobi equations
    • M.G. Crandall and P. L. Lions. Two approximations of solutions of Hamilton-Jacobi equations. Math. Comp. 43, 1-19 (1984)
    • (1984) Math. Comp. , vol.43 , pp. 1-19
    • Crandall, M.G.1    Lions, P.L.2
  • 8
    • 0000935266 scopus 로고
    • A finite difference method for the numerical computation of discontinuous solutions of the equations of fluid dynamics
    • S.K. Godunov. A finite difference method for the numerical computation of discontinuous solutions of the equations of fluid dynamics. Mat. Sb. 47, 271-290 (1959)
    • (1959) Mat. Sb. , vol.47 , pp. 271-290
    • Godunov, S.K.1
  • 9
    • 84980170156 scopus 로고
    • On finite-difference approximations and entropy conditions
    • A. Harten, J.M. Hyman, and P.D. Lax. On finite-difference approximations and entropy conditions. Comm. Pure Appl. Math. 29, 297-322 (1976)
    • (1976) Comm. Pure Appl. Math. , vol.29 , pp. 297-322
    • Harten, A.1    Hyman, J.M.2    Lax, P.D.3
  • 10
    • 0000238594 scopus 로고    scopus 로고
    • High-resolution non-oscillatory central schemes with non-staggered grids for hyperbolic conservation laws
    • G.S. Jiang, D. Levy, C.-T. Lin, S. Osher, and E. Tadmor. High-resolution non-oscillatory central schemes with non-staggered grids for hyperbolic conservation laws. SIAM J. Numer. Anal. 35, 2147-2168 (1998)
    • (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
  • 11
    • 0034503787 scopus 로고    scopus 로고
    • Weighted ENO schemes for Hamilton-Jacobi equations
    • G.S. Jiang and D. Peng. Weighted ENO schemes for Hamilton-Jacobi equations. SISSC. 21, 2126-2143 (2000)
    • (2000) SISSC , vol.21 , pp. 2126-2143
    • Jiang, G.S.1    Peng, D.2
  • 12
    • 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. SISSC. 19, 1892-1917 (1998)
    • (1998) SISSC , vol.19 , pp. 1892-1917
    • Jiang, G.S.1    Tadmor, E.2
  • 13
    • 0000997075 scopus 로고    scopus 로고
    • Numerical passage from systems of conservation laws to Hamilton-Jacobi equations
    • S. Jin and Z. Xin. Numerical passage from systems of conservation laws to Hamilton-Jacobi equations. SIAM J. Numer. Anal., pages 2385-2404 (1998)
    • (1998) SIAM J. Numer. Anal. , pp. 2385-2404
    • Jin, S.1    Xin, Z.2
  • 14
    • 0000585998 scopus 로고
    • The Cauchy problem in the large for nonlinear equations and for certain quasilinear systems of the first order with several variables
    • S.N. Kruzkov. The Cauchy problem in the large for nonlinear equations and for certain quasilinear systems of the first order with several variables. Soviet Math. Dokl. 5, 493-496 (1964)
    • (1964) Soviet Math. Dokl. , vol.5 , pp. 493-496
    • Kruzkov, S.N.1
  • 15
    • 0037567813 scopus 로고
    • General solutions of nonlinear first order with several variables. II
    • S.N. Kruzkov. General solutions of nonlinear first order with several variables. II. Math. USSR Sbornik 1, 93-116 (1967)
    • (1967) Math. USSR Sbornik , vol.1 , pp. 93-116
    • Kruzkov, S.N.1
  • 17
    • 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 Comp. Math. Math. Phys. 16, 105-119 (1976)
    • (1976) USSR Comp. Math. Math. Phys. , vol.16 , pp. 105-119
    • Kuznetsov, N.N.1
  • 18
    • 0040452394 scopus 로고
    • On stable methods for solving nonlinear first-order partial differential equations in the class of discontinuous solutions
    • J. J. H. Miller (ed.), Academic Press, London
    • N.N. Kuznetsov. On stable methods for solving nonlinear first-order partial differential equations in the class of discontinuous solutions, in Topics in Numerical Analysis III, J. J. H. Miller (ed.), Academic Press, London, pages 183-197 (1977)
    • (1977) Topics in Numerical Analysis III , pp. 183-197
    • Kuznetsov, N.N.1
  • 19
    • 0040045826 scopus 로고
    • On monotone difference approximations for a first order quasilinear equation
    • N.N. Kuznetsov and S. A. Volosin. On monotone difference approximations for a first order quasilinear equation. Soviet. Math. Dokl. 17, 1203-1206 (1976)
    • (1976) Soviet. Math. Dokl. , vol.17 , pp. 1203-1206
    • Kuznetsov, N.N.1    Volosin, S.A.2
  • 20
    • 0034505281 scopus 로고    scopus 로고
    • High-resolution non-oscillatory central schemes for Hamilton-Jacobi equations
    • C.-T. Lin and E. Tadmor. High-resolution non-oscillatory central schemes for Hamilton-Jacobi equations. SISSC 21, 2163-2186, (2000)
    • (2000) SISSC , vol.21 , pp. 2163-2186
    • Lin, C.-T.1    Tadmor, E.2
  • 22
    • 21844506272 scopus 로고
    • Convergence of MUSCL and filtered schemes for scalar conservation laws and Hamilton-Jacobi equations
    • P.L. Lions and P.E. Souganidis. Convergence of MUSCL and filtered schemes for scalar conservation laws and Hamilton-Jacobi equations. Numer. Math. 69, 441-470 (1995)
    • (1995) Numer. Math. , vol.69 , pp. 441-470
    • Lions, P.L.1    Souganidis, P.E.2
  • 23
    • 28144455569 scopus 로고
    • Non-oscillatory central differencing for hyperbolic conservation laws
    • H. Nessyahu and E. Tadmor. Non-oscillatory central differencing for hyperbolic conservation laws. JCP 87, 408-463 (1990)
    • (1990) JCP , vol.87 , pp. 408-463
    • Nessyahu, H.1    Tadmor, E.2
  • 24
    • 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 Num. Anal. 29, 1505-1519 (1992)
    • (1992) SIAM Num. Anal. , vol.29 , pp. 1505-1519
    • Nessyahu, H.1    Tadmor, E.2
  • 25
    • 0028374735 scopus 로고
    • The convergence rate of Godunov type schemes
    • H. Nessyahu, E. Tadmor, and T. Tassa. The convergence rate of Godunov type schemes. SIAM Num. Anal. 31, 1-16 (1994)
    • (1994) SIAM Num. Anal. , vol.31 , pp. 1-16
    • Nessyahu, H.1    Tadmor, E.2    Tassa, T.3
  • 26
    • 0028444534 scopus 로고
    • Convergence rate of approximate solutions to conservation laws with initial rarefactions
    • H. Nessyahu and T. Tassa. Convergence rate of approximate solutions to conservation laws with initial rarefactions. SIAM Num. Anal. 31, 628-654 (1994)
    • (1994) SIAM Num. Anal. , vol.31 , pp. 628-654
    • Nessyahu, H.1    Tassa, T.2
  • 27
    • 0002717472 scopus 로고
    • Discontinuous solutions of nonlinear differential equations
    • O.A. Oleinik Discontinuous solutions of nonlinear differential equations. Transl. AMS 26, 95-172 (1963)
    • (1963) Transl. AMS , vol.26 , pp. 95-172
    • Oleinik, O.A.1
  • 28
    • 0026204106 scopus 로고
    • High-order essential nonoscillatory schemes for Hamilton-Jacobi equations
    • S. Osher and C.-W. Shu. High-order essential nonoscillatory schemes for Hamilton-Jacobi equations. SIAM J. Numer. Anal. 28, 907-922 (1991)
    • (1991) SIAM J. Numer. Anal. , vol.28 , pp. 907-922
    • Osher, S.1    Shu, C.-W.2
  • 29
    • 0000189454 scopus 로고    scopus 로고
    • The optimal convergence rate of monotone finite difference methods for hyperbolic conservation laws
    • F. Sabac. The optimal convergence rate of monotone finite difference methods for hyperbolic conservation laws. SIAM Num Anal. 34, 2306-2318 (1997)
    • (1997) SIAM Num Anal. , vol.34 , pp. 2306-2318
    • Sabac, F.1
  • 30
    • 84966203226 scopus 로고
    • On convergence of monotone finite difference schemes with variable spatial differencing
    • R. Sanders. On convergence of monotone finite difference schemes with variable spatial differencing. Math. Comp. 40, 91-106 (1993)
    • (1993) Math. Comp. , vol.40 , pp. 91-106
    • Sanders, R.1
  • 31
    • 21144464154 scopus 로고
    • The regularized Chapman-Enskog expansion for scalar conservation laws
    • S. Schochet and E. Tadmor. The regularized Chapman-Enskog expansion for scalar conservation laws. Arch. Rational Mech. Anal. 119, 95-107 (1992)
    • (1992) Arch. Rational Mech. Anal. , vol.119 , pp. 95-107
    • Schochet, S.1    Tadmor, E.2
  • 32
    • 46549091075 scopus 로고
    • Approximation schemes for viscosity solutions of Hamilton-Jacobi equations
    • P.E. Souganidis. Approximation schemes for viscosity solutions of Hamilton-Jacobi equations. J. Diff. Eqs. 59, 1-43 (1985)
    • (1985) J. Diff. Eqs. , vol.59 , pp. 1-43
    • Souganidis, P.E.1
  • 33
    • 46549099599 scopus 로고
    • Existence of viscosity solutions of Hamilton-Jacobi equations
    • P.E. Souganidis. Existence of viscosity solutions of Hamilton-Jacobi equations. J. Diff. Eqs. 56, 345-390 (1985)
    • (1985) J. Diff. Eqs. , vol.56 , pp. 345-390
    • Souganidis, P.E.1
  • 34
    • 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 Num. Anal. 28, 891-906 (1991)
    • (1991) SIAM Num. Anal. , vol.28 , pp. 891-906
    • Tadmor, E.1
  • 35
    • 84968499102 scopus 로고
    • Total variation and error estimates for spectral viscosity approximations
    • E. Tadmor. Total variation and error estimates for spectral viscosity approximations. Math. Comp. 60, 245-256 (1993)
    • (1993) Math. Comp. , vol.60 , pp. 245-256
    • Tadmor, E.1
  • 36
    • 0001176128 scopus 로고    scopus 로고
    • Pointwise error estimates for scalar conservation laws with piecewise smooth solutions
    • E. Tadmor and T. Tang. Pointwise error estimates for scalar conservation laws with piecewise smooth solutions. SIAM J. Numer. Anal. 36, 1739-1756 (1999)
    • (1999) SIAM J. Numer. Anal. , vol.36 , pp. 1739-1756
    • Tadmor, E.1    Tang, T.2
  • 37
    • 0001400260 scopus 로고
    • On the piecewise regularity of entropy solutions to scalar conservation laws
    • E. Tadmor and T. Tassa. On the piecewise regularity of entropy solutions to scalar conservation laws. Com. PDE 18, 1631-1652 (1993)
    • (1993) Com. PDE , vol.18 , pp. 1631-1652
    • Tadmor, E.1    Tassa, T.2
  • 38
    • 84968519569 scopus 로고
    • 1-error estimate for monotone difference schemes
    • 1-error estimate for monotone difference schemes. Math. Comp. 64, 581-589 (1995)
    • (1995) Math. Comp. , vol.64 , pp. 581-589
    • Tang, T.1    Teng, Z.-H.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.