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

Luskin, Mitchell

doi:10.1090/S0025-5718-1979-0521272-6

Convergence of a finite element method for the approximation of normal modes of the oceans
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Math. Comp. 33 (1979), 493-519 Request permission

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.

References

J. H. Bramble and J. E. Osborn, Rate of convergence estimates for nonselfadjoint eigenvalue approximations, Math. Comp. 27 (1973), 525–549. MR 366029, DOI 10.1090/S0025-5718-1973-0366029-9
Philippe G. Ciarlet, Numerical analysis of the finite element method, Séminaire de Mathématiques Supérieures, No. 59 (Été 1975), Les Presses de l’Université de Montréal, Montreal, Que., 1976. MR 0495010

Sparse Matrix Computations

Jean Descloux, Mitchell Luskin, and Jacques Rappaz, Approximation of the spectrum of closed operators: the determination of normal modes of a rotating basin, Math. Comp. 36 (1981), no. 153, 137–154. MR 595047, DOI 10.1090/S0025-5718-1981-0595047-5
Jean Descloux, Nabil Nassif, and Jacques Rappaz, On spectral approximation. I. The problem of convergence, RAIRO Anal. Numér. 12 (1978), no. 2, 97–112, iii (English, with French summary). MR 483400, DOI 10.1051/m2an/1978120200971
Jean Descloux, Nabil Nassif, and Jacques Rappaz, On spectral approximation. I. The problem of convergence, RAIRO Anal. Numér. 12 (1978), no. 2, 97–112, iii (English, with French summary). MR 483400, DOI 10.1051/m2an/1978120200971
Todd Dupont, Galerkin methods for modeling gas pipelines, Constructive and computational methods for differential and integral equations (Sympos., Indiana Univ., Bloomington, Ind., 1974) Lecture Notes in Math., Vol. 430, Springer, Berlin, 1974, pp. 112–130. MR 0502035
Todd Dupont and H. H. Rachford Jr., A Galerkin method for liquid pipelines, Computing methods in applied sciences and engineering (Second Internat. Sympos., Versailles, 1975) Lecture Notes in Econom. and Math. Systems, Vol. 134, Springer, Berlin, 1976, pp. 325–337. MR 0455882
Tosio Kato, Perturbation theory for linear operators, Die Grundlehren der mathematischen Wissenschaften, Band 132, Springer-Verlag New York, Inc., New York, 1966. MR 0203473
J.-L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications. Vol. 1, Travaux et Recherches Mathématiques, No. 17, Dunod, Paris, 1968 (French). MR 0247243
Mitchell Luskin, A finite element method for first-order hyperbolic systems, Math. Comp. 35 (1980), no. 152, 1093–1112. MR 583489, DOI 10.1090/S0025-5718-1980-0583489-2
Joachim A. Nitsche and Alfred H. Schatz, Interior estimates for Ritz-Galerkin methods, Math. Comp. 28 (1974), 937–958. MR 373325, DOI 10.1090/S0025-5718-1974-0373325-9
John E. Osborn, Spectral approximation for compact operators, Math. Comput. 29 (1975), 712–725. MR 0383117, DOI 10.1090/S0025-5718-1975-0383117-3

J. Physical Oceanography

Gerhard Willem Veltkamp, Spectral properties of Hilbert space operators associated with tidal motions, University of Utrecht, Utrecht, 1960. Thesis. MR 0128212