The finite element method for infinite domains. I

Author:
Ivo Babuška

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

MSC:
Primary 65N05

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

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]**G. Fix & G. Strang, ``Fourier analysis of the finite element method in Ritz-Galerkin theory,''*Studies in Appl. Math.*, v. 48, 1969, pp. 265-273. 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. 547-585. MR**0287723 (44:4926)****[4]**M. Zlämal, ``On the finite element method,''*Numer. Math.*, v. 12, 1968, pp. 394-409. 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. 1102-1119. (Russian)**[6]**L Babuška,*Error Bounds for Finite Element Method*, Technical Note BN-630, Institute for Fluid Dynamics and Appl. Math., University of Maryland, College Park, Md., 1969;*Numer. Math.*, v. 16, 1971, pp. 322-333. MR**0288971 (44:6166)****[7]**I. Babuška,*The Rate of Convergence for the Finite Element Method*, Technical Note BN-646, Institute for Fluid Dynamics and Appl. Math., University of Maryland, College Park, Md., 1970;*SIAM J. Numer. Anal.*, v. 8, 1971, pp. 304-315. MR**0287715 (44:4918)****[8]**I. Babuška,*Finite Element Method for Domains with Corner*, Technical Note BN-636, Institute for Fluid Dynamics and Appl. Math., University of Maryland, College Park, Md., 1970;*Computing*, v. 6, 1970, pp. 264-273. MR**0293858 (45:2934)****[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]**I. Babuška,*The Finite Element Method for Elliptic Differential Equations*, Technical Note BN-653, 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. 69-107. MR**0273836 (42:8712)****[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]**I. Babuška,*Approximation by Hill Functions*, Technical Note BN-648, Institute for Fluid Dynamics and Appl. Math., University of Maryland, College Park, Md., 1970;*Comment. Math. Univ. Carolinae*, v. 11, 1970, pp. 787-811. MR**0292309 (45:1396)**

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Additional Information

DOI:
https://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