Uniform expansions for a class of finite difference schemes for elliptic boundary value problems
Author:
Harry Munz
Journal:
Math. Comp. 36 (1981), 155170
MSC:
Primary 65N05
MathSciNet review:
595048
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Abstract: For a class of finite difference schemes for the Dirichlet problem on a bounded region , the existence of uniform expansions of the approximate solution for meshlength is shown. The results also improve error bounds which Pereyra, Proskurowski, and Widlund obtained with respect to certain discrete norms.
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 [1]
 J. H. Bramble & B. E. Hubbard, "A theorem on error estimation for finite difference analogues of the Dirichlet problem for elliptic equations," Contributions to Differential Equations, v. 2, 1963, pp. 319340. MR 0152134 (27:2114)
 [2]
 J. H. Bramble & B. E. Hubbard, "Approximations of derivatives by finite difference methods in elliptic boundary value problems," Contributions to Differential Equations, v. 3, 1964, pp. 399410. MR 0166935 (29:4208)
 [3]
 P. G. Ciarlet, "Discrete maximum principle for finitedifference operators," Aequationes Math., v. 4, 1970, pp. 338352. MR 0292317 (45:1404)
 [4]
 L. Collatz, The Numerical Treatment of Differential Equations, 3rd ed., Die Grundlehren der math. Wissenschaften, Bd. 60, SpringerVerlag, BerlinGöttingenHeidelberg, 1960. MR 0109436 (22:322)
 [5]
 H. Münz, Differenzenverfahren für elliptische Randwertaufgaben mit verbesserter Randinterpolation, Diplomarbeit, Universität Tübingen, 1978. (Unpublished.)
 [6]
 V. Pereyra, "Iterated deferred corrections for nonlinear operator equations," Numer. Math., v. 10, 1967, pp. 316323. MR 0221760 (36:4812)
 [7]
 V. Pereyra, W. Proskurowski & O. Widlund, "High order fast Laplace solvers for the Dirichlet problem on general regions," Math. Comp., v. 31, 1977, pp. 116. MR 0431736 (55:4731)
 [8]
 R. S. Varga, Matrix Iterative Analysis, PrenticeHall, Englewood Cliffs, N. J., 1962. MR 0158502 (28:1725)
 [9]
 D. M. Young, Iterative Solution of Large Linear Systems, Academic Press, New York and London, 1971. MR 0305568 (46:4698)
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DOI:
http://dx.doi.org/10.1090/S00255718198105950487
PII:
S 00255718(1981)05950487
Article copyright:
© Copyright 1981 American Mathematical Society
