A finite-element method for laplace-and helmholtz-type boundary value problems with singularities

SIAM Journal on Numerical Analysis

Volumn 34, Issue 3, 1997, Pages 1037-1050

  Xiaonan, W U ^a   Han, Houde ^b  

^a HONG KONG BAPTIST UNIVERSITY   (Hong Kong)

^b TSINGHUA UNIVERSITY   (China)

Author keywords

Approximate boundary conditions at an artificial boundary; Artificial boundary; Singularity

Indexed keywords

EID: 0001238123     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/s0036142993258488     Document Type: Article

References (18)

1. I. BABUŠKA AND H. S. OH, The p-version of the finite element method for domains with corners and for infinite domains, Numer. Methods Partial Differential Equations, 6 (1990), pp. 371-392.
2. I. BABUŠKA AND M. R. ROSENZWEIG, A finite element scheme for domains with corners, Numer. Math., 20 (1972), pp. 1-21.
3. D. GIVOLI, L. RIVKIN, AND J. B. KELLER, A finite element method for domains with corners, Internat. J. Numer. Methods Engrg., 35 (1992), pp. 1329-1345.
4. C. I. GOLDSTEIN, A finite element method for solving Helmholtz type equations in waveguides and other unbounded domains, Math. Comp., 39 (1982), pp. 309-324.
5. T. M. HAGSTROM AND H. B. KELLER, Exact boundary conditions at an artificial boundary for partial differential equations in cylinders, SIAM J. Math. Anal., 17 (1986), pp. 322-341.
6. H. HAN AND X. Wu, Approximation of infinite boundary condition and its application to finite element methods, J. Comput. Math., 3 (1985), pp. 179-192.
7. H. HAN AND X. Wu, The approximation of the exact boundary conditions at an artificial boundary for linear elastic equations and its application, Math. Comp., 59 (1992), pp. 21-37.
8. K. KISHIMOTO, I. YAMAGUCHI, M. TACHIHARA, S. AOKI, AND M. SAKATA, Elastic-plastic fracture mechanics analysis by combination of boundary and finite element method, in Boundary Element, C. A. Brebbie, T. Futagami, and M. Tanaka, eds., Springer, Berlin, Heidelberg, New York, Tokyo, 1983, pp. 975-984.
9. ZI-CAl Li, A nonconforming combined method for solving Laplace's boundary value problems with singularities, Numer. Math., 49 (1986), pp. 475-497.
10. ZI-CAI Li, R. MATHON, AND P. SERMER, Boundary method for solving elliptic problems with singularities and interfaces, SIAM J. Numer. Anal., 24 (1987), pp. 487-498.
11. J. L. LIONS, Optimal control of systems governed by partial differential equations, Springer-Verlag, Berlin, Heidelberg, 1971.
12. T. R. LUCAS AND HAE-SOO OH, The method of auxiliary mapping in the finite element solutions of elliptic problems containing boundary or corner singularities, J. Comput. Phys., 108 (1993), pp. 327-432.
13. H. MOTZ, The treatment of singularities of partial differential equations by relaxation methods, Quart. Appl. Math., 4 (1946), pp. 371-377.
14. 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., 96 (1991), pp. 391-410.
15. R. W. THATCHER, The use of infinite grid refinement at singularities in the solution of Laplace's equation, Numer. Math., 25 (1976), pp. 163-178.
16. R. WAIT AND A. R. MITCHELL, Corner singularities in elliptic problems by the finite element method, J. Comput. Phys., 8 (1971), p. 45.
17. N. M. WIGLEY, On a method to subtract off a singularity at corner for the Dirichlet or Neumann problem, Math. Comp., 23 (1969), pp. 395-401.
18. C. ZIENKIEWICZ, D. W. KELLEY, AND P. BETTESS, The coupling of the finite element method and boundary solution procedures, Internat. J. Numer. Methods Engrg., 11 (1977), pp. 355-375.