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On the convergence of an algorithm for solving finite element equations
Author:
R. A. Nicolaides
Journal:
Math. Comp. 31 (1977), 892-906
MSC:
Primary 65J05; Secondary 65N30
MathSciNet review:
0488722
Full-text PDF Free Access
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Abstract: An iterative method of multiple grid type is proposed for solving general finite element systems. It is proved that the method can produce a solution to the equations in arithmetical operations where N is the number of unknowns.
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S. Bahvalov, Convergence of a relaxation method under natural
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P. G. CIARLET & P. A. RAVIART, La Methode des Eléments Finis Pour les Problèmes aux Limites Elliptiques, Chap. 1, Univ. Paris VI, Lab. Analyse Numerique, 1974.
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P. Fedorenko, On the speed of convergence of an iteration
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(31 #6386)
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Kronsjö, A note on the “nested iterations”
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(58 #19255)
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S.
G. Mikhlin, The numerical performance of variational methods,
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A. Nicolaides, On multiple grid and related techniques for solving
discrete elliptic systems, J. Computational Phys. 19
(1975), no. 4, 418–431. MR 0413541
(54 #1655)
- [7]
R.
A. Nicolaides, On the observed rate of convergence of
an iterative method applied to a model elliptic difference
equation, Math. Comp. 32
(1978), no. 141, 127–133. MR 0458932
(56 #17131), http://dx.doi.org/10.1090/S0025-5718-1978-0458932-0
- [1]
- N. S. BAHVALOV, "On the convergence of a relaxation method under natural constraints on an elliptic operator," Ž. Vyčisl. Mat. i Mat. Fiz., v. 6, 1966, pp. 861-883. (Russian) MR 35 #6378. MR 0215538 (35:6378)
- [2]
- P. G. CIARLET & P. A. RAVIART, La Methode des Eléments Finis Pour les Problèmes aux Limites Elliptiques, Chap. 1, Univ. Paris VI, Lab. Analyse Numerique, 1974.
- [3]
- R. P. FEDORENKO, "The speed of convergence of an iteration process," Ž. Vyčisl. Mat. i Mat. Fiz., v. 4, 1964, pp. 559-564. (Russian) MR 31 #6386. MR 0182163 (31:6386)
- [4]
- LYDIA KRONSKÖ, "A note on the "nested iterations" method," BIT, v. 15, 1975, pp. 107-110. MR 0502089 (58:19255)
- [5]
- S. G. MIHLIN, The Numerical Performance of Variational Methods, English transl., Noordhoff, Groningen, 1971. MR 34 #3747; 43 #4236. MR 0278506 (43:4236)
- [6]
- R. A. NICOLAIDES, "On multiple grid and related techniques for solving discrete elliptic systems," J. Computational Phys., v. 19, 1975, pp. 418-431. MR 0413541 (54:1655)
- [7]
- R. A. NICOLAIDES, "On the observed rate of convergence of an iterative method, applied to a model elliptic difference equation," Math. Comp. (To appear.) MR 0458932 (56:17131)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0025-5718-1977-0488722-3
PII:
S 0025-5718(1977)0488722-3
Article copyright:
© Copyright 1977 American Mathematical Society
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