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Some grid refinement schemes for hyperbolic equations with piecewise constant coefficients


Authors: T. Lin, J. Sochacki, R. Ewing and J. George
Journal: Math. Comp. 56 (1991), 61-86
MSC: Primary 65M50; Secondary 35L45, 35R05
DOI: https://doi.org/10.1090/S0025-5718-1991-1052100-6
MathSciNet review: 1052100
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Abstract: Discontinuities in the coefficients of hyperbolic equations occur both naturally and artificially and must be treated in numerical schemes. Schemes for handling these discontinuities are derived. An interesting stability result is derived and the schemes are shown to be exact under certain restrictions.


References [Enhancements On Off] (What's this?)

  • [1] M. Berger, Stability of interfaces with mesh refinement, Math. Comp. 45 (1985), 301-318. MR 804925 (87d:65097)
  • [2] J. Oliger, Hybrid difference methods for the initial boundary-value problem for hyperbolic equations, Math. Comp. 30 (1976), 724-738. MR 0428727 (55:1747)
  • [3] D. L. Brown, A note on the numerical solution of the wave equation with piecewise smooth coefficients, Math. Comp. 42 (1984), 369-391. MR 736442 (85h:65194)
  • [4] G. Browning, H.-O. Kreiss, and J. Oliger, Mesh refinement, Math. Comp. 27 (1973), 29-39. MR 0334542 (48:12861)
  • [5] M. Ciment, Stable difference schemes with uneven mesh spacings, Math. Comp. 25 (1971), 219-227. MR 0300470 (45:9516)
  • [6] M. de Moura, Variable grids for finite difference schemes in numerical weather prediction, Pontificia Universidade Catolica de Rio de Janeiro, 1987.
  • [7] B. Gustafsson, H.-O. Kreiss, and A. Sundström, Stability theory of difference approximations for mixed initial boundary value problems. II, Math. Comp. 26 (1972), 649-686. MR 0341888 (49:6634)
  • [8] G. Starius, On composite mesh difference methods for hyperbolic differential equations, Numer. Math. 35 (1980), 241-255. MR 592156 (82b:65089)
  • [9] A. Sundström, Efficient numerical methods for solving wave propagation equations for nonhomogeneous media, Stockholm Report, 1974.
  • [10] L. Trefethen, Stability of finite difference models containing two boundaries or interfaces, Math. Comp. 45 (1985), 279-300. MR 804924 (87h:65158)
  • [11] -, Instability of difference methods for hyperbolic initial boundary value problems, Comm. Pure Appl. Math. 37 (1984), 329-367. MR 739924 (86f:65162)
  • [12] L. Trefethen, Wave propagation and stability for finite difference schemes, Ph.D. Dissertation, Department of Computer Science, Stanford University, 1982.
  • [13] R. Vichnevetsky, Wave propagation analysis of difference schemes for hyperbolic equations: a review, Internat. J. Numer. Methods Fluids 7 (1987), 409-452. MR 888909 (88b:65107)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1991-1052100-6
Article copyright: © Copyright 1991 American Mathematical Society

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