The finite element method for infinite domains. I
Author:
Ivo Babuška
Journal:
Math. Comp. 26 (1972), 111
MSC:
Primary 65N05
MathSciNet review:
0298969
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Abstract: Numerical methods (finite element methods) for the approximate solution of elliptic partial differential equations on unbounded domains are considered, and error bounds, with respect to the number of unknowns which have to be determined, are proven.
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George
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G. Strang & G. Fix, ``A Fourier analysis of the finite element variational method.'' (To appear.)
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Ivo
Babuška, Errorbounds for finite element method, Numer.
Math. 16 (1970/1971), 322–333. MR 0288971
(44 #6166)
 [7]
Ivo
Babuška, The rate of convergence for the finite element
method, SIAM J. Numer. Anal. 8 (1971), 304–315.
MR
0287715 (44 #4918)
 [8]
Ivo
Babuška, Finite element method for domains with
corners, Computing (Arch. Elektron. Rechnen) 6
(1970), 264–273 (English, with German summary). MR 0293858
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 [9]
I. Babušska, Numerical Solution of Boundary Value Problems by the Perturbed Variation Principle, Technical Note BN624, Institute for Fluid Dynamics and Appl. Math., University of Maryland, College Park, Md., 1969.
 [10]
I. Bauška, The Finite Element Method for Elliptic Equations with Discontinuous Coefficients, Technical Note BN631, Institute for Fluid Dynamics and Appl. Math., University of Maryland, College Park, Md., 1969; Computing, v. 5, 1970, pp. 207213.
 [11]
Ivo
Babuška, The finite element method for elliptic differential
equations, Numerical Solution of Partial Differential Equations, II
(SYNSPADE 1970) (Proc. Sympos., Univ. of Maryland, College Park, Md., 1970)
Academic Press, New York, 1971, pp. 69–106. MR 0273836
(42 #8712)
 [12]
O. C. Zienkiewicz, The Finite Element Method in Structural and Continuous Mechanics, McGrawHill, New York and London, 1970.
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Y. R. Rashid, On Computational Methods in Solid Mechanics and Stress Analysis, Conference on Effective Use of Comp. in the Nuclear Industry, Knoxville, Tenn., April 2123, 1969.
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Approximation by hill functions, Comment. Math. Univ. Carolinae
11 (1970), 787–811. MR 0292309
(45 #1396)
 [1]
 G. Fix & G. Strang, ``Fourier analysis of the finite element method in RitzGalerkin theory,'' Studies in Appl. Math., v. 48, 1969, pp. 265273. MR 41 #2944. MR 0258297 (41:2944)
 [2]
 G. Strang & G. Fix, ``A Fourier analysis of the finite element variational method.'' (To appear.)
 [3]
 G. Strang, The Finite Element Method and Approximation Theory, Numerical Solution of Partial Differential Equations. II (SYNSPADE, 1970), Academic Press, New York and London, 1971, pp. 547585. MR 0287723 (44:4926)
 [4]
 M. Zlämal, ``On the finite element method,'' Numer. Math., v. 12, 1968, pp. 394409. MR 39 #5074. MR 0243753 (39:5074)
 [5]
 L. A. Oganesjan & L. A. Ruchovec, ``A study of rates of convergence of some variational difference schemes for elliptic equations of second order in a two dimensional domain with smooth boundary,'' Ž. Vyčisl. Mat. i Mat. Fiz., v. 9, 1969, pp. 11021119. (Russian)
 [6]
 L Babuška, Error Bounds for Finite Element Method, Technical Note BN630, Institute for Fluid Dynamics and Appl. Math., University of Maryland, College Park, Md., 1969; Numer. Math., v. 16, 1971, pp. 322333. MR 0288971 (44:6166)
 [7]
 I. Babuška, The Rate of Convergence for the Finite Element Method, Technical Note BN646, Institute for Fluid Dynamics and Appl. Math., University of Maryland, College Park, Md., 1970; SIAM J. Numer. Anal., v. 8, 1971, pp. 304315. MR 0287715 (44:4918)
 [8]
 I. Babuška, Finite Element Method for Domains with Corner, Technical Note BN636, Institute for Fluid Dynamics and Appl. Math., University of Maryland, College Park, Md., 1970; Computing, v. 6, 1970, pp. 264273. MR 0293858 (45:2934)
 [9]
 I. Babušska, Numerical Solution of Boundary Value Problems by the Perturbed Variation Principle, Technical Note BN624, Institute for Fluid Dynamics and Appl. Math., University of Maryland, College Park, Md., 1969.
 [10]
 I. Bauška, The Finite Element Method for Elliptic Equations with Discontinuous Coefficients, Technical Note BN631, Institute for Fluid Dynamics and Appl. Math., University of Maryland, College Park, Md., 1969; Computing, v. 5, 1970, pp. 207213.
 [11]
 I. Babuška, The Finite Element Method for Elliptic Differential Equations, Technical Note BN653, Institute for Fluid Dynamics and Appl. Math., University of Maryland, College Park, Md., 1970, Numerical Solution of Partial Differential Equations. II (SYNSPADE, 1970), Academic Press, New York and London, 1971, pp. 69107. MR 0273836 (42:8712)
 [12]
 O. C. Zienkiewicz, The Finite Element Method in Structural and Continuous Mechanics, McGrawHill, New York and London, 1970.
 [13]
 Y. R. Rashid, On Computational Methods in Solid Mechanics and Stress Analysis, Conference on Effective Use of Comp. in the Nuclear Industry, Knoxville, Tenn., April 2123, 1969.
 [14]
 I. Babuška, Approximation by Hill Functions, Technical Note BN648, Institute for Fluid Dynamics and Appl. Math., University of Maryland, College Park, Md., 1970; Comment. Math. Univ. Carolinae, v. 11, 1970, pp. 787811. MR 0292309 (45:1396)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197202989692
PII:
S 00255718(1972)02989692
Keywords:
Numerical element method,
numerical method for elliptic equations and unbounded domains
Article copyright:
© Copyright 1972
American Mathematical Society
