Convergence of a finite element method for the approximation of normal modes of the oceans
HTML articles powered by AMS MathViewer
- by Mitchell Luskin PDF
- 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 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.
- 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 T. DUPONT, Personal communication.
- 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 G. W. PLATZMAN, "Normal modes of the Atlantic and Indian Oceans," J. Physical Oceanography, v. 5, 1975, pp. 201-221. 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. R. SCOTT, Personal communication.
- Gerhard Willem Veltkamp, Spectral properties of Hilbert space operators associated with tidal motions, University of Utrecht, Utrecht, 1960. Thesis. MR 0128212
Additional Information
- © Copyright 1979 American Mathematical Society
- 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