The finite element method for infinite domains. I

Author:
Ivo Babuška

Journal:
Math. Comp. **26** (1972), 1-11

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.

**[1]**George Fix and Gilbert Strang,*Fourier analysis of the finite element method in Ritz-Galerkin theory.*, Studies in Appl. Math.**48**(1969), 265–273. MR**0258297****[2]**G. Strang & G. Fix, ``A Fourier analysis of the finite element variational method.'' (To appear.)**[3]**Gilbert Strang,*The finite element method and approximation theory*, Numerical Solution of Partial Differential Equations, II (SYNSPADE 1970) (Proc. Sympos., Univ. of Maryland, College Park, Md., 1970) Academic Press, New York, 1971, pp. 547–583. MR**0287723****[4]**Miloš Zlámal,*On the finite element method*, Numer. Math.**12**(1968), 394–409. MR**0243753****[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. 1102-1119. (Russian)**[6]**Ivo Babuška,*Error-bounds for finite element method*, Numer. Math.**16**(1970/1971), 322–333. MR**0288971****[7]**Ivo Babuška,*The rate of convergence for the finite element method*, SIAM J. Numer. Anal.**8**(1971), 304–315. MR**0287715****[8]**Ivo Babuška,*Finite element method for domains with corners*, Computing (Arch. Elektron. Rechnen)**6**(1970), 264–273 (English, with German summary). MR**0293858****[9]**I. Babušska,*Numerical Solution of Boundary Value Problems by the Perturbed Variation Principle*, Technical Note BN-624, 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 BN-631, Institute for Fluid Dynamics and Appl. Math., University of Maryland, College Park, Md., 1969;*Computing*, v. 5, 1970, pp. 207-213.**[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****[12]**O. C. Zienkiewicz,*The Finite Element Method in Structural and Continuous Mechanics*, McGraw-Hill, 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 21-23, 1969.**[14]***Approximation by hill functions*, Comment. Math. Univ. Carolinae**11**(1970), 787–811. MR**0292309**

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0025-5718-1972-0298969-2

Keywords:
Numerical element method,
numerical method for elliptic equations and unbounded domains

Article copyright:
© Copyright 1972
American Mathematical Society