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
Fulltext PDF Free Access
Abstract 
References 
Similar Articles 
Additional Information
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 .
 [1]
Numerical solution of ordinary and partial differential
equations., Based on a Summer School held in Oxford, AugustSeptember
1961, Pergamon Press, Oxford, 1962. MR 0146969
(26 #4488)
 [2]
S. Gerschgorin, ``Fehlerabschätzung für das Differenzenverfahren für Lösung partieller Differentialgleichungen,'' Z. Angew. Math. Mech., v. 10, 1930, pp. 373382.
 [3]
Pentti
Laasonen, On the behavior of the solution of the Dirichlet problem
at analytic corners, Ann. Acad. Sci. Fenn. Ser. A. I.
1957 (1957), no. 241, 13. MR 0091405
(19,964a)
 [4]
Hans
Lewy, Developments at the confluence of analytic boundary
conditions, Univ. California Publ. Math. (N.S.) 1
(1950), 247–280. MR 0040431
(12,691c)
 [5]
R.
Sherman Lehman, Developments at an analytic corner of solutions of
elliptic partial differential equations, J. Math. Mech.
8 (1959), 727–760. MR 0105552
(21 #4291)
 [6]
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.
 [7]
Neil
M. Wigley, Asymptotic expansions at a corner of solutions of mixed
boundary value problems, J. Math. Mech. 13 (1964),
549–576. MR 0165227
(29 #2516)
 [8]
George
E. Forsythe and Wolfgang
R. Wasow, Finitedifference methods for partial differential
equations, Applied Mathematics Series, John Wiley & Sons Inc., New
York, 1960. MR
0130124 (23 #B3156)
 [1]
 L. Fox, (Editor), Numerical Solution of Ordinary and Partial Differential Equations, Pergamon Press, London and AddisonWesley, Reading, Mass., 1962, pp. 302303. MR 26 #4488. MR 0146969 (26:4488)
 [2]
 S. Gerschgorin, ``Fehlerabschätzung für das Differenzenverfahren für Lösung partieller Differentialgleichungen,'' Z. Angew. Math. Mech., v. 10, 1930, pp. 373382.
 [3]
 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)
 [4]
 H. Lewy, ``Developments at the confluence of analytic boundary conditions,'' Univ. of Calif. Publ. Math., v. 1, 1950, pp. 247280. MR 0040431 (12:691c)
 [5]
 R. S. Lehman, ``Developments at an analytic corner of solutions of elliptic partial differential equations,'' J. Math. Mech., v. 8, 1959, pp. 727760. MR 21 #4291. MR 0105552 (21:4291)
 [6]
 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.
 [7]
 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)
 [8]
 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)
Similar Articles
Retrieve articles in Mathematics of Computation
with MSC:
65.66
Retrieve articles in all journals
with MSC:
65.66
Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718196902452230
PII:
S 00255718(1969)02452230
Article copyright:
© Copyright 1969 American Mathematical Society
