Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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CLASSIFICATION OF SINGULAR SOLUTIONS FOR THE POISSON PROBLEM WITH VARIOUS BOUNDARY CONDITIONS

  • Kim, Seok-Chan (Department of Applied Mathematics, Changwon National University) ;
  • Woo, Gyung-Soo (Department of Applied Mathematics, Changwon National University) ;
  • Kong, Soo-Ryoun (Department of Applied Mathematics, Changwon National University)
  • Received : 2009.08.19
  • Accepted : 2009.10.01
  • Published : 2009.12.25
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Abstract

The precise form of singular functions, singular function representation and the extraction form for the stress intensity factor play an important role in the singular function methods to deal with the domain singularities for the Poisson problems with most common boundary conditions, e.q. Dirichlet or Mixed boundary condition [2, 4]. In this paper we give an elementary step to get the singular functions of the solution for Poisson problem with Neumann boundary condition or Robin boundary condition. We also give singular function representation and the extraction form for the stress intensity with a result showing the number of singular functions depending on the boundary conditions.

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References

  1. W. E. BOYCE, R. C. DIPRIMA, Elementary Differential Equations and Boundary value Problems, 8th ed.
  2. Z. CAI, S. KIM, A finite element method using singular functions for the poisson equation: Corner singularities, SIAM J. Numer. Anal., 39:(2001), 286-299. https://doi.org/10.1137/S0036142999355945
  3. Z. CAI, S. KIM, and B.-C. SHIN, Solution methods for the Poisson equation: Comer singularities, SIAM J. Sci. Comput., SIMI J. SCI. COMPUT., 23:(2001), 672-682. https://doi.org/10.1137/S1064827500372778
  4. Z. CAl, S. KIM, S. KIM, AND S. KONG, A finite element method using singular functions for Poisson equations: mixed boundary conditions, Computer Methods Appl. Mach. Engrg., 195 (2006), no. 19-22, 2635-2648.. https://doi.org/10.1016/j.cma.2005.06.004
  5. P. GRISVARD, Elliptic Problems in Nonsmooth Domains, Pitman, Boston, MA, 1985.
  6. S.C. KIM, J.H. PYO, S.S. XIE, S. YI, Notes on new singular function method for domain singularities, Honam Math. J. 29 (2007), no. 4, 701-721. https://doi.org/10.5831/HMJ.2007.29.4.701