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The finite element method with nonuniform mesh sizes for unbounded domains. (English) Zbl 0467.65058


MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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[1] Ivo Babuška and A. K. Aziz, Survey lectures on the mathematical foundations of the finite element method, The mathematical foundations of the finite element method with applications to partial differential equations (Proc. Sympos., Univ. Maryland, Baltimore, Md., 1972) Academic Press, New York, 1972, pp. 1 – 359. With the collaboration of G. Fix and R. B. Kellogg. · Zbl 0268.65052
[2] Philippe G. Ciarlet, The finite element method for elliptic problems, North-Holland Publishing Co., Amsterdam-New York-Oxford, 1978. Studies in Mathematics and its Applications, Vol. 4. · Zbl 0383.65058
[3] Gilbert Strang and George J. Fix, An analysis of the finite element method, Prentice-Hall, Inc., Englewood Cliffs, N. J., 1973. Prentice-Hall Series in Automatic Computation. · Zbl 0356.65096
[4] Ivo Babuška, The finite element method for infinite domains. I, Math. Comp. 26 (1972), 1 – 11. · Zbl 0257.35002
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[7] A. H. Schatz and L. B. Wahlbin, Maximum norm estimates in the finite element method on plane polygonal domains. I, Math. Comp. 32 (1978), no. 141, 73 – 109. , https://doi.org/10.1090/S0025-5718-1978-0502065-1 A. H. Schatz and L. B. Wahlbin, Maximum norm estimates in the finite element method on plane polygonal domains. II. Refinements, Math. Comp. 33 (1979), no. 146, 465 – 492. · Zbl 0382.65058
[8] Ivo Babuška, Finite element method for domains with corners, Computing (Arch. Elektron. Rechnen) 6 (1970), 264 – 273 (English, with German summary). · Zbl 0224.65031
[9] S. C. Eisenstat and M. H. Schultz, Computational aspects of the finite element method, The mathematical foundations of the finite element method with applications to partial differential equations (Proc. Sympos., Univ. Maryland, Baltimore, Md., 1972) Academic Press, New York, 1972, pp. 505 – 524. · Zbl 0265.65053
[10] R. W. Thatcher, The use of infinite grid refinements at singularities in the solution of Laplace’s equation, Numer. Math. 25 (1975/76), no. 2, 163 – 178. · Zbl 0299.65061 · doi:10.1007/BF01462270
[11] O. D. Kellogg, Foundations of Potential Theory, Ungar, New York, 1929.
[12] George Hsiao and R. C. MacCamy, Solution of boundary value problems by integral equations of the first kind, SIAM Rev. 15 (1973), 687 – 705. · Zbl 0235.45006 · doi:10.1137/1015093
[13] Martin Schechter, General boundary value problems for elliptic partial differential equations, Comm. Pure Appl. Math. 12 (1959), 457 – 486. · Zbl 0087.30204 · doi:10.1002/cpa.3160120305
[14] A. Bayliss, M. Gunzberger & E. Turkel, Boundary Conditions for the Numerical Solution of Elliptic Equations in Exterior Regions, ICASE Report 80-1, 1979.
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