A singular function boundary integral method for the laplace equation

Communications in Numerical Methods in Engineering

Volumn 12, Issue 2, 1996, Pages 127-134

  Georgiou, Georgios C ^a   Olson, Lorraine ^b   Smyrlis, Yiorgos S ^a  

^a UNIVERSITY OF CYPRUS   (Cyprus)

^b UNIVERSITY OF NEBRASKA LINCOLN   (United States)

Author keywords

Boundary integral method; Laplace equation; Singularities

Indexed keywords

APPROXIMATION THEORY; BOUNDARY CONDITIONS; CONVERGENCE OF NUMERICAL METHODS; ESTIMATION; FUNCTIONS; INTEGRAL EQUATIONS; LAGRANGE MULTIPLIERS; LAPLACE TRANSFORMS; PROBLEM SOLVING;

BOUNDARY INTEGRAL METHOD; LAPLACE EQUATION; LOCAL ASYMPTOTIC EXPANSION; MOTZ PROBLEM; SINGULAR FUNCTIONS; SINGULARITIES;

NUMERICAL METHODS;

EID: 0030082646     PISSN: 10698299     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1099-0887(199602)12:2<127::AID-CNM959>3.0.CO;2-I     Document Type: Article

References (13)

1. L. G. Olson, G. C. Georgiou and W. W. Schultz, 'An efficient finite element method for treating singularities in Laplace's equation', J. Comput. Phys., 6, (2), 391-409 (1991).
2. G. J. Fix, Finite Elements. Theory and Application, D. L. Dwoyer, M. Y. Hussaini and R. G. Voigt (eds), Springer-Verlag, New York, 1988, Chap. 3.
3. G. C. Georgiou, L. G. Olson and W. W. Schultz, "The integrated singular basis function method for the stick-slip and the die-swell problems', Int. j. numer. methods fluids, 13, 1251 (1991).
4. H. Motz, "The treatment of singularities in relaxation methods', Q. Appl. Math., 4, 371 (1946).
5. R. Wait and A. R. Mitchell, 'Corner singularities in elliptic problems by finite element methods', J. Comput. Phys., 8, 45 (1971).
6. S. N. Mergelyan, 'Uniform approximations to functions of a complex variable', Am. Math. Soc. Transl. Ser. 1, 3, 294-391 (1962).
7. J. B. Rosser and N. Papamichael, 'A power series solution of a harmonic mixed boundary value problem', MRC Technical Summary, Rept. 1405, University of Wisconsin, 1975.
8. N. Papamichael, 'Numerical conformal mapping onto a rectangle with applications to the solution of Laplacian problems', J. Comput. Appl. Math., 28, 63-83 (1989).
9. Morley, L. S. D., 'Finite element solution of boundary value problems with non-removable singularities', Philos. Trans. R. Soc. Lond. A, Math. Phys. Sci., 257A, 1252 (1973).
10. Yamamoto, Y., 'Finite element approach with the aid of analytical solutions', in Recent Advances in Matrix Methods of Structural Analysis and Design, 1971, pp. 85-103.
11. Symm, G. T., "Treatment of singularities in the solution of Laplace's equation by an integral equation method', National Physical Laboratory Report NAC31, 1973.
12. N. Papamichael and G. T. Symm, 'Numerical techniques for two-dimensional Laplacian problems', Comput. Methods. Appl. Mech. Eng., 6, 175-194 (1975).
13. Z. -C. Li, R. Mathon and P. Sermer, 'Boundary methods for solving elliptic problems with singularities and interfaces', SIAM J. Numer. Anal. 24, (3), 487-498 (1987).