메뉴 건너뛰기




Volumn 188, Issue 2, 2003, Pages 543-572

An adaptive mesh redistribution method for nonlinear Hamilton-Jacobi equations in two- and three-dimensions

Author keywords

Finite difference method; Hamilton Jacobi equations; Level set equations; Moving adaptive grid method

Indexed keywords

MESH GENERATION; NONLINEAR EQUATIONS; NUMERICAL METHODS;

EID: 0038346370     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0021-9991(03)00192-X     Document Type: Article
Times cited : (61)

References (37)
  • 1
    • 0030521036 scopus 로고    scopus 로고
    • Numerical discretization of first order Hamilton-Jacobi equations on triangular meshes
    • R. Abgrall, Numerical discretization of first order Hamilton-Jacobi equations on triangular meshes, Commun. Pure Appl. Math. 49 (1996) 1339-1373.
    • (1996) Commun. Pure Appl. Math. , vol.49 , pp. 1339-1373
    • Abgrall, R.1
  • 2
    • 0034197010 scopus 로고    scopus 로고
    • High order numerical discretization for Hamilton-Jacobi equations on triangular meshes
    • S. Augoula, R. Abgrall, High order numerical discretization for Hamilton-Jacobi equations on triangular meshes, J. Sci. Comp. 15 (2000) 197-229.
    • (2000) J. Sci. Comp. , vol.15 , pp. 197-229
    • Augoula, S.1    Abgrall, R.2
  • 3
    • 0037689751 scopus 로고    scopus 로고
    • Adaptive mesh redistribution method based on Godunov's scheme
    • B.N. Azarenok, S.A. Ivanenko, T. Tang, Adaptive mesh redistribution method based on Godunov's scheme, Commun. Math. Sci. 1 (2003) 152 179.
    • (2003) Commun. Math. Sci. , vol.1 , pp. 152-179
    • Azarenok, B.N.1    Ivanenko, S.A.2    Tang, T.3
  • 4
    • 0002437983 scopus 로고    scopus 로고
    • Numerical schemes for the Hamilton-Jacobi and Level set equations on triangulated domains
    • T.J. Barth, J.A. Sethian, Numerical schemes for the Hamilton-Jacobi and Level set equations on triangulated domains, J. Comput. Phys. 145 (1998) 1-40.
    • (1998) J. Comput. Phys. , vol.145 , pp. 1-40
    • Barth, T.J.1    Sethian, J.A.2
  • 5
    • 49049134162 scopus 로고
    • Adaptive zoning for singular problems in two dimensions
    • J.U. Brackbill, J.S. Saltzman, Adaptive zoning for singular problems in two dimensions, J. Comput. Phys. 46 (1982) 342-368.
    • (1982) J. Comput. Phys. , vol.46 , pp. 342-368
    • Brackbill, J.U.1    Saltzman, J.S.2
  • 6
    • 84967758647 scopus 로고
    • Viscosity solutions of Hamilton-Jacobi equations
    • M.G. Crandall, P.L. Lions, Viscosity solutions of Hamilton-Jacobi equations, Trans. Am. Math. Soc. 277 (1983) 1-42.
    • (1983) Trans. Am. Math. Soc. , vol.277 , pp. 1-42
    • Crandall, M.G.1    Lions, P.L.2
  • 7
    • 0000076512 scopus 로고    scopus 로고
    • Runge-Kutta discontinuous Galerkin methods for convection-dominated problems
    • B. Cockburn, C.-W. Shu, Runge-Kutta discontinuous Galerkin methods for convection-dominated problems, J. Sci. Comp. 16 (2001) 173-261.
    • (2001) J. Sci. Comp. , vol.16 , pp. 173-261
    • Cockburn, B.1    Shu, C.-W.2
  • 8
    • 84967708673 scopus 로고
    • User's guide to viscosity solutions of second order partial differential equations
    • M.G. Crandall, H. Ishi, P.L. Lions, User's guide to viscosity solutions of second order partial differential equations, Bull. Am. Math. Soc. 27 (1992) 1-67.
    • (1992) Bull. Am. Math. Soc. , vol.27 , pp. 1-67
    • Crandall, M.G.1    Ishi, H.2    Lions, P.L.3
  • 9
    • 84966245867 scopus 로고
    • Two approximations of solutions of Hamilton-Jacobi equations
    • M.G. Crandall, P.L. Lions, Two approximations of solutions of Hamilton-Jacobi equations, Math. Comput. 43 (1984) 1-19.
    • (1984) Math. Comput. , vol.43 , pp. 1-19
    • Crandall, M.G.1    Lions, P.L.2
  • 11
    • 84972528479 scopus 로고
    • The heat equation shrinks embedded plane curves to round points
    • M. Grayson, The heat equation shrinks embedded plane curves to round points, J. Diff. Geom. 26 (1987) 285-314.
    • (1987) J. Diff. Geom. , vol.26 , pp. 285-314
    • Grayson, M.1
  • 12
    • 0033296133 scopus 로고    scopus 로고
    • A discontinuous Galerkin finite element method for Hamilton-Jacobi equations
    • C.Q. Hu, C.W. Shu, A discontinuous Galerkin finite element method for Hamilton-Jacobi equations, SIAM J. Sci. Comput. 21 (2000) 666-690.
    • (2000) SIAM J. Sci. Comput. , vol.21 , pp. 666-690
    • Hu, C.Q.1    Shu, C.W.2
  • 13
    • 0034503787 scopus 로고    scopus 로고
    • Weighted ENO schemes for Hamilton-Jacobi equations
    • G.S. Jiang, D.P. Peng, Weighted ENO schemes for Hamilton-Jacobi equations, SIAM J. Sci. Comput. 21 (2000) 2126-2143.
    • (2000) SIAM J. Sci. Comput. , vol.21 , pp. 2126-2143
    • Jiang, G.S.1    Peng, D.P.2
  • 14
    • 0030161771 scopus 로고    scopus 로고
    • Efficient implementation of weighted ENO schemes
    • G. Jiang, C.-W. Shu, Efficient implementation of weighted ENO schemes, J. Comput. Phys. 126 (1996) 202-228.
    • (1996) J. Comput. Phys. , vol.126 , pp. 202-228
    • Jiang, G.1    Shu, C.-W.2
  • 15
    • 0035322540 scopus 로고    scopus 로고
    • On the convergence rate of operator splitting for Hamilton-Jacobi equations with source terms
    • E.R. Jakobsen, K.H. Karlsen, N.H. Risebro, On the convergence rate of operator splitting for Hamilton-Jacobi equations with source terms, SIAM J. Numer. Anal. 39 (2001) 499-518.
    • (2001) SIAM J. Numer. Anal. , vol.39 , pp. 499-518
    • Jakobsen, E.R.1    Karlsen, K.H.2    Risebro, N.H.3
  • 16
    • 0000997075 scopus 로고    scopus 로고
    • Numerical passage from systems of conservation laws to Hamilton-Jacobi equations, and relaxing schemes
    • S. Jin, Z.P. Xin, Numerical passage from systems of conservation laws to Hamilton-Jacobi equations, and relaxing schemes, SIAM J. Numer. Anal. 35 (1998) 2385-2404.
    • (1998) SIAM J. Numer. Anal. , vol.35 , pp. 2385-2404
    • Jin, S.1    Xin, Z.P.2
  • 17
    • 0347987814 scopus 로고    scopus 로고
    • New high-resolution central schemes for nonlinear conservation laws and convective-diffusion equations
    • A. Kurganov, E. Tadmor, New high-resolution central schemes for nonlinear conservation laws and convective-diffusion equations, J. Comput. Phys. 160 (2000) 214-282.
    • (2000) J. Comput. Phys. , vol.160 , pp. 214-282
    • Kurganov, A.1    Tadmor, E.2
  • 18
    • 0000356257 scopus 로고    scopus 로고
    • New high-resolution semi-discrete central schemes for Hamilton-Jacobi equations
    • A. Kurganov, E. Tadmor, New high-resolution semi-discrete central schemes for Hamilton-Jacobi equations, J. Comput. Phys. 160 (2000) 720-742.
    • (2000) J. Comput. Phys. , vol.160 , pp. 720-742
    • Kurganov, A.1    Tadmor, E.2
  • 19
    • 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) 105-119.
    • (1976) USSR Comput. Math. Math. Phys. , vol.16 , pp. 105-119
    • Kuznetsov, N.N.1
  • 20
    • 0000314925 scopus 로고    scopus 로고
    • High-resolution conservative algorithms for advection in incompressible flow
    • R.J. LeVeque, High-resolution conservative algorithms for advection in incompressible flow, SIAM J. Numer. Anal. 33 (1996) 627-665.
    • (1996) SIAM J. Numer. Anal. , vol.33 , pp. 627-665
    • LeVeque, R.J.1
  • 21
    • 0000592595 scopus 로고
    • Weighted essentially nonoscillatory schemes
    • X.-D. Liu, S. Osher, T. Chan, Weighted essentially nonoscillatory schemes, J. Comput. Phys. 115 (1994) 200-212.
    • (1994) J. Comput. Phys. , vol.115 , pp. 200-212
    • Liu, X.-D.1    Osher, S.2    Chan, T.3
  • 22
    • 0000501759 scopus 로고    scopus 로고
    • Moving mesh methods in multiple dimensions based on harmonic maps
    • R. Li, T. Tang, P.W. Zhang, Moving mesh methods in multiple dimensions based on harmonic maps, J. Comput. Phys. 170 (2001) 562-588.
    • (2001) J. Comput. Phys. , vol.170 , pp. 562-588
    • Li, R.1    Tang, T.2    Zhang, P.W.3
  • 23
    • 0037052068 scopus 로고    scopus 로고
    • A moving mesh finite element algorithm for singular problems in two and three space dimensions
    • R. Li, T. Tang, P.-W. Zhang, A moving mesh finite element algorithm for singular problems in two and three space dimensions, J. Comput. Phys. 177 (2002) 365-393.
    • (2002) J. Comput. Phys. , vol.177 , pp. 365-393
    • Li, R.1    Tang, T.2    Zhang, P.-W.3
  • 24
    • 0034505281 scopus 로고    scopus 로고
    • High-resolution non-oscillatory central schemes for Hamilton-Jacobi equations
    • C.T. Lin, E. Tadmor, High-resolution non-oscillatory central schemes for Hamilton-Jacobi equations, SIAM J. Sci. Comput. 21 (2000) 2163-2186.
    • (2000) SIAM J. Sci. Comput. , vol.21 , pp. 2163-2186
    • Lin, C.T.1    Tadmor, E.2
  • 25
    • 0035580662 scopus 로고    scopus 로고
    • 1-stability and error estimates for approximate Hamilton-Jacobi solutions
    • 1-stability and error estimates for approximate Hamilton-Jacobi solutions, Numer. Math. 87 (2001) 701-735.
    • (2001) Numer. Math. , vol.87 , pp. 701-735
    • Lin, C.T.1    Tadmor, E.2
  • 26
    • 44749084234 scopus 로고
    • Fronts propagating with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulations
    • S. Osher, J. Sethian, Fronts propagating with curvature dependent speed: algorithms based on Hamilton-Jacobi formulations, J. Comput. Phys. 79 (1988) 12-49.
    • (1988) J. Comput. Phys. , vol.79 , pp. 12-49
    • Osher, S.1    Sethian, J.2
  • 27
    • 0026204106 scopus 로고
    • High-order essentially nonoscillatory schemes for Hamilton-Jacobi equations
    • S. Osher, C.W. Shu, High-order essentially nonoscillatory schemes for Hamilton-Jacobi equations, SIAM J. Numer. Anal. 28 (1991) 907-922.
    • (1991) SIAM J. Numer. Anal. , vol.28 , pp. 907-922
    • Osher, S.1    Shu, C.W.2
  • 28
    • 0032325185 scopus 로고    scopus 로고
    • Uniqueness and error estimates in first order quasilinear conservation laws via the kinetic entropy defect measure
    • B. Perthame, Uniqueness and error estimates in first order quasilinear conservation laws via the kinetic entropy defect measure, J. Math. Pure Appl. 77 (1998) 1055-1064.
    • (1998) J. Math. Pure Appl. , vol.77 , pp. 1055-1064
    • Perthame, B.1
  • 29
    • 0003661003 scopus 로고    scopus 로고
    • Cambridge University Press, New York
    • J. Sethian, Level Set Methods, Cambridge University Press, New York, 1996.
    • (1996) Level Set Methods
    • Sethian, J.1
  • 30
    • 0034774698 scopus 로고    scopus 로고
    • A moving mesh method for one-dimensional hyperbolic conservation laws
    • J.M. Stockie, J.A. Mackenzie, R.D. Russell, A moving mesh method for one-dimensional hyperbolic conservation laws, SIAM J. Sci. Comput. 22 (2001) 1791-1813.
    • (2001) SIAM J. Sci. Comput. , vol.22 , pp. 1791-1813
    • Stockie, J.M.1    Mackenzie, J.A.2    Russell, R.D.3
  • 31
    • 0001568854 scopus 로고
    • Efficient implement of essentially non-oscillatory shock-wave schemes, II
    • C.-W. Shu, S. Osher, Efficient implement of essentially non-oscillatory shock-wave schemes, II, J. Comput. Phys. 83 (1989) 32-78.
    • (1989) J. Comput. Phys. , vol.83 , pp. 32-78
    • Shu, C.-W.1    Osher, S.2
  • 32
    • 0001176128 scopus 로고    scopus 로고
    • Pointwise error estimates for scalar conservation laws with piecewise smooth solutions
    • E. Tadmor, T. Tang, Pointwise error estimates for scalar conservation laws with piecewise smooth solutions, SIAM J. Numer. Anal. 36 (1999) 1739-1758.
    • (1999) SIAM J. Numer. Anal. , vol.36 , pp. 1739-1758
    • Tadmor, E.1    Tang, T.2
  • 33
    • 0038704068 scopus 로고    scopus 로고
    • Moving mesh methods for one- and two-dimensional hyperbolic conservation laws
    • H.Z. Tang, T. Tang, Moving mesh methods for one- and two-dimensional hyperbolic conservation laws, SIAM J. Numer. Anal. 41 (2003) 487-515.
    • (2003) SIAM J. Numer. Anal. , vol.41 , pp. 487-515
    • Tang, H.Z.1    Tang, T.2
  • 34
    • 84968519569 scopus 로고
    • 1-error estimate for monotone difference schemes
    • 1-error estimate for monotone difference schemes, Math. Comp. (1995) 581-589.
    • (1995) Math. Comp. , pp. 581-589
    • Tang, T.1    Teng, Z.H.2
  • 35
    • 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. Comput. Phys. 32 (1979) 101-136.
    • (1979) J. Comput. Phys. , vol.32 , pp. 101-136
    • van Leer, B.1
  • 36
    • 49949139816 scopus 로고
    • Numerical solution of the quasi-linear Poisson equation
    • A. Winslow, Numerical solution of the quasi-linear Poisson equation, J. Comput. Phys. 1 (1967) 149-172.
    • (1967) J. Comput. Phys. , vol.1 , pp. 149-172
    • Winslow, A.1
  • 37
    • 0038070190 scopus 로고    scopus 로고
    • High order WENO schemes for Hamilton-Jacobi equations on triangular meshes
    • Y.-T. Zhang, C.-W. Shu, High order WENO schemes for Hamilton-Jacobi equations on triangular meshes, SIAM J. Sci. Comp. 24 (2003) 1005-1030.
    • (2003) SIAM J. Sci. Comp. , vol.24 , pp. 1005-1030
    • Zhang, Y.-T.1    Shu, C.-W.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.