On a method to subtract off a singularity at a corner for the Dirichlet or Neumann problem
Author:
Neil M. Wigley
Journal:
Math. Comp. 23 (1969), 395401
MSC:
Primary 65.66
MathSciNet review:
0245223
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Abstract: Let be a plane domain partly bounded by two line segments which meet at the origin and form there an interior angle . Let be a solution in of Poisson's equation such that either or (the normal derivative) takes prescribed values on the boundary segments. Let be sufficiently smooth away from the corner and bounded at the corner. Then for each positive integer there exists a function which satisfies a related Poisson equation and which satisfies related boundary conditions such that is times continuously differentiable at the corner. If is an integer may be found explicitly in terms of the data of the problem for .
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 S. Gerschgorin, ``Fehlerabschätzung für das Differenzenverfahren für Lösung partieller Differentialgleichungen,'' Z. Angew. Math. Mech., v. 10, 1930, pp. 373382.
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 P. Laasonen, ``On the behavior of the solution of the Dirichlet problem at analytic corners,'' Ann. Acad. Sci. Fenn. A I, v. 408, 1957, pp. 316. MR 0091405 (19:964a)
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 H. Lewy, ``Developments at the confluence of analytic boundary conditions,'' Univ. of Calif. Publ. Math., v. 1, 1950, pp. 247280. MR 0040431 (12:691c)
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 W. R. Wasow, ``Asymptotic development of the solution of Dirichlet's problem at analytic corners,'' Duke Math. J., v. 24, 1957, pp. 4756. MR 18, 568.
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 N. M. Wigley, ``Asymptotic expansions at a corner of solutions of mixed boundary value problems,'' J. Math. Mech., v. 13, 1964, pp. 549576. MR 29 #2516. MR 0165227 (29:2516)
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 G. E. Forsythe & W. R. Wasow, FiniteDifference Methods for Partial Differential Equations, Appl. Math. Series, Wiley, New York, 1960, pp. 283288. MR 23 B3156. MR 0130124 (23:B3156)
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DOI:
http://dx.doi.org/10.1090/S00255718196902452230
PII:
S 00255718(1969)02452230
Article copyright:
© Copyright 1969
American Mathematical Society
