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Convergence of a finite element method for the approximation of normal modes of the oceans


Author: Mitchell Luskin
Journal: Math. Comp. 33 (1979), 493-519
MSC: Primary 86A05; Secondary 65N30
DOI: https://doi.org/10.1090/S0025-5718-1979-0521272-6
MathSciNet review: 521272
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Abstract: This paper gives optimal order error estimates for the approximation of the spectral properties of a variant of the shallow water equations by a finite element procedure recently proposed by Platzman. General results on the spectral approximation of unbounded, selfadjoint operators are also given in this paper.


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  • [1] J. H. BRAMBLE & J. E. OSBORN, "Rate of convergence estimates for nonselfadjoint eigenvalue approximations," Math. Comp., v. 27, 1973, pp. 525-549. MR 0366029 (51:2280)
  • [2] P. G. CIARLET, Numerical Analysis of the Finite Element Method, Univeristy of Montreal Press, Montreal, 1976. MR 0495010 (58:13778)
  • [3] A. K. CLINE, G. H. GOLUB & G. W. PLATZMAN, "Calculation of normal modes of oceans using a Lanczos method," Sparse Matrix Computations, J. Bunch and D. Rose (eds.), Academic Press, New York, 1976, pp. 409-429.
  • [4] J. DESCLOUX, M. LUSKIN & J. RAPPAZ, "Approximation of the spectrum of closed operators. The determination of normal modes of a rotating basin". (To appear.) MR 595047 (83h:65123)
  • [5] J. DESCLOUX, N. NASSIF & J. RAPPAZ, "On spectral approximation. Part 1. The problem of convergence," R.A.I.R.O. Numerical Analysis, v. 12, no. 2, 1978, pp. 97-112. MR 0483400 (58:3404a)
  • [6] J. DESCLOUX, N. NASSIF & J. RAPPAZ, "On spectral approximation. Part 2. Error estimates for the Galerkin method," R.A.I.R.O. Numerical Analysis, v. 12, no. 2, 1978, pp. 113-119. MR 0483401 (58:3404b)
  • [7] T. DUPONT, Personal communication.
  • [8] 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)
  • [9] T. DUPONT & H. RACHFORD, JR., "A Galerkin method for liquid pipelines," Computational Methods in Applied Sciences and Engineering, Lecture Notes in Econ. and Math. Systems, vol. 134, Springer-Verlag, Berlin and New York, 1976. MR 0455882 (56:14116)
  • [10] T. KATO, Perturbation Theory for Linear Operators, Die Grundelehren der Math. Wissenschaften, Band 132, Springer-Verlag, New York, 1966. MR 0203473 (34:3324)
  • [11] J. L. LIONS & E. MAGENES, Problèmes aux Limites Non Homogènes et Applications, vol. 1, Dunod, Paris, 1968. MR 0247243 (40:512)
  • [12] M. LUSKIN, "A finite element method for first order hyperbolic systems." (To appear.) MR 583489 (81i:65092)
  • [13] J. NITSCHE & A. SCHATZ, "Interior estimates for Ritz-Galerkin methods," Math. Comp., v. 28, 1974, pp. 937-958. MR 0373325 (51:9525)
  • [14] J. E. OSBORN, "Spectral approximation for compact operators," Math. Comp., v. 29, 1975, pp. 712-725. MR 0383117 (52:3998)
  • [15] G. W. PLATZMAN, "Normal modes of the Atlantic and Indian Oceans," J. Physical Oceanography, v. 5, 1975, pp. 201-221.
  • [16] G. W. PLATZMAN, "Normal modes of the world Ocean. Part 1. Design of a finiteelement baratropic model," J. Physical Oceanography, v. 8, 1978, pp. 323-343.
  • [17] R. SCOTT, Personal communication.
  • [18] G. W. VELTKAMP, Spectral Properties of Hilbert Space Operators Associated with Tidal Motions, Drukkerij Wed. G. Van Soest, Amsterdam, 1960. MR 0128212 (23:B1256)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1979-0521272-6
Article copyright: © Copyright 1979 American Mathematical Society

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