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A finite element method for first-order hyperbolic systems

Author: Mitchell Luskin
Journal: Math. Comp. 35 (1980), 1093-1112
MSC: Primary 65N30; Secondary 65M15, 76N15
MathSciNet review: 583489
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Abstract: A new finite element method is proposed for the numerical solution of a class of initial-boundary value problems for first-order hyperbolic systems in one space dimension. An application of our procedure to a system modeling gas flow in a pipe is discussed. Asymptotic error estimates are derived in the $ {L^2}$ norm in space.

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  • [1] J. DOUGLAS, JR., T. DUPONT & L. WAHLBIN, "Optimal $ {L_\infty }$ error estimates for Galerkin approximations to solutions of two-point boundary value problems," Math. Comp., v. 29, 1975, pp. 475-483. MR 0371077 (51:7298)
  • [2] T. DUPONT, "Galerkin methods for modeling gas pipelines," Constructive and Computational Methods for Differential and Integral Equations, Lecture Notes in Math., Vol. 430, Springer-Verlag, Berlin and New York, 1974. MR 0502035 (58:19223)
  • [3] T. DUPONT, "Galerkin methods for first order hyperbolics: an example," SIAM J. Numer. Anal., v. 10, 1973, pp. 890-899. MR 0349046 (50:1540)
  • [4] T. DUPONT & L. WAHLBIN, "$ {L^2}$ optimality of weighted $ {H^1}$ projections into piecewise polynomial spaces," Manuscript, Dept. of Math., Univ. of Chicago, 1974.
  • [5] G. HEDSTROM, "The Galerkin method based on Hermite cubics," SIAM J. Numer. Anal., v. 16, 1979, pp. 385-393. MR 530476 (80i:65116)
  • [6] M. LEES, "A linear three level difference scheme for quasilinear parabolic equations," Math. Comp., v. 20, 1966, pp. 516-522. MR 0207224 (34:7040)
  • [7] M. LUSKIN, "On the existence of global smooth solutions for a model equation for fluid flow in a pipe," Manuscript, Dept. of Math., Ecole Polytechnique Fédérale de Lausanne, 1980. MR 639688 (83g:76078)
  • [8] M. LUSKIN, "A finite element method for first order hyperbolic systems in two space variables," Manuscript, Dept. of Math., Univ. of Michigan, 1978.
  • [9] G. PLATZMAN, "Normal modes of the world ocean. Part 1. Design of a finite-element barotropic model," J. Phys. Oceanogr., v. 8, 1979, pp. 323-343.
  • [10] H. RACHFORD, JR., "Two-level discrete-time Galerkin approximations for second order nonlinear parabolic partial differential equations," SIAM J. Numer. Anal., v. 10, 1973, pp. 1010-1026. MR 0339519 (49:4277)
  • [11] G. STRANG & G. FIX, An Analysis of the Finite Element Method, Prentice-Hall, Englewood Cliffs, N.J., 1973. MR 0443377 (56:1747)
  • [12] V. STREETER, Fluid Mechanics, 5th ed., McGraw-Hill, New York, 1971.
  • [13] L. WAHLBIN, "A dissipative Galerkin method applied to some quasilinear hyperbolic equations," R.A.I.R.O. Anal. Numer., v. 8, 1974, pp. 109-117. MR 0368447 (51:4688)

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Article copyright: © Copyright 1980 American Mathematical Society

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