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.
 [1]
J.
H. Bramble and B.
E. Hubbard, A theorem on error estimation for finite difference
analogues of the Dirichlet problem for elliptic equations,
Contributions to Differential Equations 2 (1963),
319–340. MR 0152134
(27 #2114)
 [2]
J.
H. Bramble and B.
E. Hubbard, Approximation of derivatives by finite difference
methods in elliptic boundary value problems, Contributions to
Differential Equations 3 (1964), 399–410. MR 0166935
(29 #4208)
 [3]
Philippe
G. Ciarlet, Discrete maximum principle for finitedifference
operators, Aequationes Math. 4 (1970), 338–352.
MR
0292317 (45 #1404)
 [4]
Lothar
Collatz, The numerical treatment of differential equations. 3d
ed, Translated from a supplemented version of the 2d German edition by
P. G. Williams. Die Grundlehren der mathematischen 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 (Unpublished.)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]
Victor
Pereyra, Iterated deferred corrections for nonlinear operator
equations, Numer. Math. 10 (1967), 316–323. MR 0221760
(36 #4812)
 [7]
Victor
Pereyra, Wlodzimierz
Proskurowski, and Olof
Widlund, High order fast Laplace solvers for
the Dirichlet problem on general regions, Math.
Comp. 31 (1977), no. 137, 1–16. MR 0431736
(55 #4731), http://dx.doi.org/10.1090/S0025571819770431736X
 [8]
Richard
S. Varga, Matrix iterative analysis, PrenticeHall, Inc.,
Englewood Cliffs, N.J., 1962. MR 0158502
(28 #1725)
 [9]
David
M. Young, Iterative solution of large linear systems, Academic
Press, New YorkLondon, 1971. MR 0305568
(46 #4698)
 [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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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198105950487
PII:
S 00255718(1981)05950487
Article copyright:
© Copyright 1981
American Mathematical Society
